Question

let f and g be defined by the table to the right. find the following.
\\(\sqrt{f(-4)-f(-3)}-g(-1)^{2}+f(-5)+g(-1)\cdot g(-4)\\)
\\(\sqrt{f(-4)-f(-3)}-g(-1)^{2}+f(-5)+g(-1)\cdot g(-4)=\square\\) (simplify your answer.)

Explanation:

Step1: Find function - values from table

From the table, $f(-4) = 0$, $f(-3)=-9$, $g(-1)= - 2$, $f(-5)=2$, $g(-4)=9$.

Step2: Calculate the square - root part

Substitute $f(-4)$ and $f(-3)$ into $\sqrt{f(-4)-f(-3)}$:
$\sqrt{0-(-9)}=\sqrt{9} = 3$.

Step3: Calculate the square part

Calculate $[g(-1)]^{2}$:
$[g(-1)]^{2}=(-2)^{2}=4$.

Step4: Calculate the product part

Calculate $g(-1)\cdot g(-4)$:
$g(-1)\cdot g(-4)=(-2)\times9=-18$.

Step5: Calculate the whole expression

Substitute all the values into the original expression:
$\sqrt{f(-4)-f(-3)}-[g(-1)]^{2}+f(-5)+g(-1)\cdot g(-4)=3 - 4+2+( - 18)$.
First, $3-4=-1$, then $-1 + 2=1$, and finally $1+( - 18)=-17$.

Answer:

$-17$