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$Given the definitions of f(x) and g(x) below, find the value of g(f(2)). {:[f(x)=-5x+3],[g(x)=2x^(2)+5x-14]:} Answer:$

Given the definitions of $f(x)$ and $g(x)$ below, find the value of $g(f(2))$ . $\newline$ $\begin{array}{l} f(x)=-5 x+3 \\ g(x)=2 x^{2}+5 x-14 \end{array}$ $\newline$ Answer:

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Solve absolute value inequalities

Full solution

Q. Given the definitions of

f(x)

and

g(x)

below, find the value of

g(f(2))

.

\newline

\begin{array}{l} f(x)=-5 x+3 \\ g(x)=2 x^{2}+5 x-14 \end{array}

\newline

Answer:

Find $f(2)$ : First, we need to find the value of $f(2)$ by substituting $x$ with $2$ in the function $f(x)$ . $\newline$ $f(2) = -5(2) + 3$
Calculate $f(2)$ : Now, let's perform the calculation for $f(2)$ . $\newline$ $f(2) = -10 + 3$ $\newline$ $f(2) = -7$
Find $g(f(2))$ : Next, we need to find the value of $g(f(2))$ . Since we have found that $f(2) = -7$ , we will substitute $x$ with $-7$ in the function $g(x)$ . $\newline$ $g(f(2)) = g(-7) = 2(-7)^2 + 5(-7) - 14$
Calculate $g(-7)$ : Now, let's perform the calculation for $g(-7)$ .
$g(-7) = 2(49) + 5(-7) - 14$
$g(-7) = 98 - 35 - 14$
Find $g(-7)$ : Finally, we add and subtract the numbers to find the value of $g(-7)$ .
$g(-7) = 98 - 35 - 14$
$g(-7) = 63 - 14$
$g(-7) = 49$

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