Question

evaluate the function at the given value of the variable. f(x)=3x^{2}+3 a. f(5) b. f(-4) a. f(5)=

Explanation:

Step1: Substitute x = 5

Substitute x = 5 into f(x)=3x² + 3.
$f(5)=3\times5^{2}+3$

Step2: Calculate 5²

$5^{2}=25$, so $f(5)=3\times25 + 3$.

Step3: Calculate 3×25

$3\times25 = 75$, then $f(5)=75+3$.

Step4: Calculate the sum

$f(5)=78$.

Step5: Substitute x = - 4

Substitute x=-4 into f(x)=3x² + 3.
$f(-4)=3\times(-4)^{2}+3$

Step6: Calculate (-4)²

$(-4)^{2}=16$, so $f(-4)=3\times16+3$.

Step7: Calculate 3×16

$3\times16 = 48$, then $f(-4)=48 + 3$.

Step8: Calculate the sum

$f(-4)=51$.

Answer:

a. $f(5)=78$
b. $f(-4)=51$