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$Given the definitions of f(x) and g(x) below, find the value of g(f(-1)). {:[f(x)=x^(2)-3x-10],[g(x)=3x-10]:} Answer:$

Given the definitions of $f(x)$ and $g(x)$ below, find the value of $g(f(-1))$ . $\newline$ $\begin{array}{l} f(x)=x^{2}-3 x-10 \\ g(x)=3 x-10 \end{array}$ $\newline$ Answer:

Full solution

Q. Given the definitions of

f(x)

and

g(x)

below, find the value of

g(f(-1))

\newline

\begin{array}{l} f(x)=x^{2}-3 x-10 \\ g(x)=3 x-10 \end{array}

\newline

Answer:

Given Functions: We are given two functions: $\newline$ $f(x) = x^2 - 3x - 10$ $\newline$ $g(x) = 3x - 10$ $\newline$ We need to find the value of $g(f(-1))$ . First, we will calculate $f(-1)$ .
Calculate $f(-1)$ : Substitute $x = -1$ into the function $f(x)$ .
$f(-1) = (-1)^2 - 3(-1) - 10$
Calculate the value of $f(-1)$ .
$f(-1) = 1 + 3 - 10$
$f(-1) = 4 - 10$
$f(-1) = -6$
Calculate $g(f(-1))$ : Now that we have the value of $f(-1)$ , we will substitute it into the function $g(x)$ to find $g(f(-1))$ . $\newline$ Substitute $f(-1) = -6$ into $g(x)$ . $\newline$ $g(f(-1)) = g(-6)$ $\newline$ $g(-6) = 3(-6) - 10$ $\newline$ Calculate the value of $g(-6)$ . $\newline$ $g(-6) = -18 - 10$ $\newline$ $f(-1)$ $0$