Question

4.) $f(3) = 4(3) - 7$ $f(3) = \underline{\quad\quad}$ $f(-5) = 4(-5) - 7$ $f(-5) = \underline{\quad\quad}$
5.) $f(4) = -3(4) + 10$ $f(4) = \underline{\quad\quad}$ $f(-9) = -3(-9) + 10$ $f(-9) = \underline{\quad\quad}$
6.) $g(6) = 6^2 + 5(6) - 1$ $g(6) = \underline{\quad\quad}$ $g(-4) = (-4)^2 + 5(-4) - 1$ $g(-4) = \underline{\quad\quad}$
7.) $h(5) = -2(5)^2 - 3(5) + 8$ $h(5) = \underline{\quad\quad}$ $h(0) = -2(0)^2 - 3(0) + 8$ $h(0) = \underline{\quad\quad}$
8.) $f(5) = 2(5) + 7$ $f(5) = \underline{\quad\quad}$ $f(18) = 2(18) + 7$ $f(18) = \underline{\quad\quad}$ $f(-5) = 2(-5) + 7$ $f(-5) = \underline{\quad\quad}$
9.) $g(-2) = 9 - 2(-2)$ $g(-2) = \underline{\quad\quad}$ $g(10) = 9 - 2(10)$ $g(10) = \underline{\quad\quad}$ $g(-1) = 9 - 2(-1)$ $g(-1) = \underline{\quad\quad}$
10.) $f(2) = 3(2^2) - 1$ $f(2) = \underline{\quad\quad}$ $f(4) = 3(4^2) - 1$ $f(4) = \underline{\quad\quad}$ $f(-3) = 3*(-3)^2 - 1$ $f(-3) = \underline{\quad\quad}$
11.) $h(1) = (1)^2 + 8(1) - 3$ $h(1) = \underline{\quad\quad}$ $h(5) = (10)^2 + 8(5) - 3$ $h(5) = \underline{\quad\quad}$ $h(-1) = (-2)^2 + 8(-2) - 3$ $h(-2) = \underline{\quad\quad}$
12.) $f(4) = \frac{4^2 + 2(4)}{4 - 5}$ $f(4) = \underline{\quad\quad}$ $f(7) = \frac{7^2 + 2(7)}{7 - 5}$ $f(7) = \underline{\quad\quad}$ $f(-2) = \frac{(-2)^2 + 2(-2)}{-2 - 5}$ $f(-2) = \underline{\quad\quad}$
13.) $g(5) = -5^2 + 3(5) + 2$ $g(5) = \underline{\quad\quad}$ $g(-3) = -(-3)^2 + 3(-3) + 2$ $g(-3) = \underline{\quad\quad}$ $g(0) = -0^2 + 3(0) + 2$ $g(0) = \underline{\quad\quad}$

Explanation:

Step1: Calculate \( f(3) \)

Given \( f(3)=4(3) - 7 \), first multiply \( 4\times3 = 12 \), then subtract 7: \( 12 - 7 = 5 \). So \( f(3)=5 \).

Step2: Calculate \( f(-5) \)

Given \( f(-5)=4(-5)-7 \), first multiply \( 4\times(-5)=-20 \), then subtract 7: \( -20 - 7=-27 \). So \( f(-5)=-27 \).

Step3: Calculate \( f(4) \)

Given \( f(4)=-3(4)+10 \), first multiply \( -3\times4 = -12 \), then add 10: \( -12 + 10=-2 \). So \( f(4)=-2 \).

Step4: Calculate \( f(-9) \)

Given \( f(-9)=-3(-9)+10 \), first multiply \( -3\times(-9)=27 \), then add 10: \( 27 + 10 = 37 \). So \( f(-9)=37 \).

Step5: Calculate \( g(6) \)

Given \( g(6)=6^{2}+5(6)-1 \), first calculate \( 6^{2}=36 \), \( 5\times6 = 30 \), then add and subtract: \( 36+30 - 1=65 \). So \( g(6)=65 \).

Step6: Calculate \( g(-4) \)

Given \( g(-4)=(-4)^{2}+5(-4)-1 \), first calculate \( (-4)^{2}=16 \), \( 5\times(-4)=-20 \), then add and subtract: \( 16-20 - 1=-5 \). So \( g(-4)=-5 \).

Step7: Calculate \( h(5) \)

Given \( h(5)=-2(5)^{2}-3(5)+8 \), first calculate \( 5^{2}=25 \), \( -2\times25=-50 \), \( -3\times5=-15 \), then add and subtract: \( -50-15 + 8=-57 \). So \( h(5)=-57 \).

Step8: Calculate \( h(0) \)

Given \( h(0)=-2(0)^{2}-3(0)+8 \), since \( 0^{2}=0 \), \( -2\times0 = 0 \), \( -3\times0 = 0 \), so \( 0 - 0+8 = 8 \). So \( h(0)=8 \).

Step9: Calculate \( f(5) \)

Given \( f(5)=2(5)+7 \), multiply \( 2\times5 = 10 \), then add 7: \( 10 + 7=17 \). So \( f(5)=17 \).

Step10: Calculate \( f(18) \)

Given \( f(18)=2(18)+7 \), multiply \( 2\times18 = 36 \), then add 7: \( 36+7 = 43 \). So \( f(18)=43 \).

Step11: Calculate \( f(-5) \) (second \( f(-5) \))

Given \( f(-5)=2(-5)+7 \), multiply \( 2\times(-5)=-10 \), then add 7: \( -10 + 7=-3 \). So \( f(-5)=-3 \).

Step12: Calculate \( g(-2) \)

Given \( g(-2)=9-2(-2) \), multiply \( -2\times(-2)=4 \), then subtract: \( 9 + 4=13 \). So \( g(-2)=13 \).

Step13: Calculate \( g(10) \)

Given \( g(10)=9-2(10) \), multiply \( 2\times10 = 20 \), then subtract: \( 9-20=-11 \). So \( g(10)=-11 \).

Step14: Calculate \( g(-1) \)

Given \( g(-1)=9-2(-1) \), multiply \( -2\times(-1)=2 \), then subtract: \( 9 + 2=11 \). So \( g(-1)=11 \).

Step15: Calculate \( F(2) \)

Given \( F(2)=3(2^{2})-1 \), first calculate \( 2^{2}=4 \), \( 3\times4 = 12 \), then subtract 1: \( 12-1 = 11 \). So \( F(2)=11 \).

Step16: Calculate \( F(4) \)

Given \( F(4)=3(4^{2})-1 \), first calculate \( 4^{2}=16 \), \( 3\times16 = 48 \), then subtract 1: \( 48-1 = 47 \). So \( F(4)=47 \).

Step17: Calculate \( F(-3) \)

Given \( F(-3)=3\times(-3)^{2}-1 \), first calculate \( (-3)^{2}=9 \), \( 3\times9 = 27 \), then subtract 1: \( 27-1 = 26 \). So \( F(-3)=26 \).

Step18: Calculate \( h(1) \)

Given \( h(1)=(1)^{2}+8(1)-3 \), first calculate \( 1^{2}=1 \), \( 8\times1 = 8 \), then add and subtract: \( 1+8 - 3=6 \). So \( h(1)=6 \).

Step19: Calculate \( h(5) \) (second \( h(5) \))

Given \( h(5)=(10)^{2}+8(5)-3 \), first calculate \( 10^{2}=100 \), \( 8\times5 = 40 \), then add and subtract: \( 100+40 - 3=137 \). So \( h(5)=137 \).

Step20: Calculate \( h(-2) \) (second \( h(-2) \))

Given \( h(-2)=(-2)^{2}+8(-2)-3 \), first calculate \( (-2)^{2}=4 \), \( 8\times(-2)=-16 \), then add and subtract: \( 4-16 - 3=-15 \). Wait, the original problem has a typo? Wait, the function is \( h(-1)=(-2)^{2}+8(-2)-3 \), no, the first part is \( h(-2)=(1)^{2}+8(1)-3 \)? Wait, no, the problem says \( h(-2)=(1)^{2}+8(1)-3 \)? Wait, maybe a typo, but following the given: \( h(-2)=(1)^{2}+8(1)-3=1 + 8-3 = 6 \)? Wait, no, the user's problem: "11.) \( h(-2)=(1)^{2}+8(1)-3 \) \( h(1)=\underline{\quad} \) \( h(5)=(10)^{2}+8(5)-3 \) \( h(5)=\underline{\quad} \) \( h(-1)=(-2)^{2}+8(-2)-3 \) \( h(-2)=\underline{\quad} \)". Oh, so \( h(1)=(1)^{2}+8(1)-3=1 + 8-3 = 6 \), \( h(5)=10^{2}+8\times5 - 3=100 + 40-3 = 137 \), \( h(-2) \) is from \( h(-1) \)'s formula? Wait, no, the user's writing is a bit messy. But let's proceed with the given:

For \( h(1) \): \( (1)^{2}+8(1)-3=1 + 8-3 = 6 \).

For \( h(5) \): \( 10^{2}+8\times5 - 3=100 + 40-3 = 137 \).

For \( h(-2) \): Wait, the formula is \( h(-1)=(-2)^{2}+8(-2)-3 \), but the question is \( h(-2)=\underline{\quad} \). Maybe a typo, but if we take the formula as \( h(-2)=(-2)^{2}+8(-2)-3=4-16 - 3=-15 \).

Step21: Calculate \( f(4) \) (third \( f(4) \))

Given \( f(4)=\frac{4^{2}+2(4)}{4 - 5} \), first calculate numerator: \( 16+8 = 24 \), denominator: \( 4 - 5=-1 \), so \( \frac{24}{-1}=-24 \). So \( f(4)=-24 \).

Step22: Calculate \( f(7) \)

Given \( f(7)=\frac{7^{2}+2(7)}{7 - 5} \), numerator: \( 49+14 = 63 \), denominator: \( 7 - 5 = 2 \), so \( \frac{63}{2}=31.5 \)? Wait, no, the user's writing: \( f(7)=\frac{7^{2}+2(7)}{7 - 5}\) with a 63 over 2, so \( \frac{63}{2}=31.5 \)? But the user wrote \( f(7)=\underline{-63} \)? Wait, no, the denominator is \( 7 - 5 = 2 \), so \( 63\div2 = 31.5 \), but maybe a typo. Wait, the user's original: \( f(7)=\frac{7^{2}+2(7)}{7 - 5}\) with 63 over 2, so \( f(7)=31.5 \)? But the user's handwritten is 63 over 2, then \( f(7)=\underline{-63} \)? No, maybe denominator is \( 7 - 5 = 2 \), so 63/2=31.5. But maybe the user made a mistake. However, following the calculation: \( 7^{2}=49 \), \( 2\times7 = 14 \), numerator 49 + 14 = 63, denominator 7 - 5 = 2, so \( 63/2 = 31.5 \).

Step23: Calculate \( f(-2) \)

Given \( f(-2)=\frac{(-2)^{2}+2(-2)}{-2 - 5} \), numerator: \( 4-4 = 0 \), denominator: \( -7 \), so \( \frac{0}{-7}=0 \). So \( f(-2)=0 \).

Step24: Calculate \( G(5) \)

Given \( G(5)=-5^{2}+3(5)+2 \), note that \( -5^{2}=-25 \) (not \( (-5)^{2} \)), then \( 3\times5 = 15 \), so \( -25+15 + 2=-8 \). Wait, the user's handwritten is 42, which is wrong. Wait, \( -5^{2}=-25 \), \( 3\times5 = 15 \), so \( -25 + 15+2=-8 \). But the user wrote 42, maybe a mistake. But let's calculate correctly: \( -5^{2}+3\times5 + 2=-25 + 15+2=-8 \).

Step25: Calculate \( G(-3) \)

Given \( G(-3)=-(-3)^{2}+3(-3)+2 \), first calculate \( (-3)^{2}=9 \), so \( -9+(-9)+2=-16 \). So \( G(-3)=-16 \).

Step26: Calculate \( G(0) \)

Given \( G(0)=-0^{2}+3(0)+2 \), \( -0 + 0+2=2 \). So \( G(0)=2 \).

Answer:

1. \( f(3)=\boldsymbol{5} \), \( f(-5)=\boldsymbol{-27} \)
2. \( f(4)=\boldsymbol{-2} \), \( f(-9)=\boldsymbol{37} \)
3. \( g(6)=\boldsymbol{65} \), \( g(-4)=\boldsymbol{-5} \)
4. \( h(5)=\boldsymbol{-57} \), \( h(0)=\boldsymbol{8} \)
5. \( f(5)=\boldsymbol{17} \), \( f(18)=\boldsymbol{43} \), \( f(-5)=\boldsymbol{-3} \)
6. \( g(-2)=\boldsymbol{13} \), \( g(10)=\boldsymbol{-11} \), \( g(-1)=\boldsymbol{11} \)
7. \( F(2)=\boldsymbol{11} \), \( F(4)=\boldsymbol{47} \), \( F(-3)=\boldsymbol{26} \)
8. \( h(1)=\boldsymbol{6} \), \( h(5)=\boldsymbol{137} \), \( h(-2)=\boldsymbol{-15} \) (corrected)
9. \( f(4)=\boldsymbol{-24} \), \( f(7)=\boldsymbol{31.5} \) (or \( \frac{63}{2} \)), \( f(-2)=\boldsymbol{0} \)
10. \( G(5)=\boldsymbol{-8} \) (corrected), \( G(-3)=\boldsymbol{-16} \), \( G(0)=\boldsymbol{2} \)

(Note: Some handwritten answers in the original image have calculation errors; the above are the correct results based on the given functions.)