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$Given the definitions of f(x) and g(x) below, find the value of f(g(4)). {:[f(x)=x^(2)+4x+11],[g(x)=3x-11]:} Answer:$

Given the definitions of $f(x)$ and $g(x)$ below, find the value of $f(g(4))$ . $\newline$ $\begin{array}{l} f(x)=x^{2}+4 x+11 \\ g(x)=3 x-11 \end{array}$ $\newline$ Answer:

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Transformations of quadratic functions

Full solution

Q. Given the definitions of

f(x)

and

g(x)

below, find the value of

f(g(4))

.

\newline

\begin{array}{l} f(x)=x^{2}+4 x+11 \\ g(x)=3 x-11 \end{array}

\newline

Answer:

Find $g(4)$ : First, we need to find the value of $g(4)$ by substituting $x$ with $4$ in the function $g(x)$ . $\newline$ Calculation: $g(4) = 3(4) - 11$ $\newline$ $g(4) = 12 - 11$ $\newline$ $g(4) = 1$
Substitute $g(4)$ into $f(x)$ : Now that we have the value of $g(4)$ , we need to substitute this value into the function $f(x)$ to find $f(g(4))$ .
Calculation: $f(g(4)) = f(1)$
$f(1) = (1)^2 + 4(1) + 11$
$f(1) = 1 + 4 + 11$
$f(1) = 16$

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