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$Given the definitions of f(x) and g(x) below, find the value of (g@f)(4). {:[f(x)=2x^(2)-2x-15],[g(x)=3x-4]:} Answer:$

Given the definitions of $f(x)$ and $g(x)$ below, find the value of $(g \circ f)(4)$ . $\newline$ $\begin{array}{l} f(x)=2 x^{2}-2 x-15 \\ g(x)=3 x-4 \end{array}$ $\newline$ Answer:

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Divide numbers written in scientific notation

Full solution

Q. Given the definitions of

f(x)

and

g(x)

below, find the value of

(g \circ f)(4)

.

\newline

\begin{array}{l} f(x)=2 x^{2}-2 x-15 \\ g(x)=3 x-4 \end{array}

\newline

Answer:

Find $f(4)$ : First, we need to find the value of $f(4)$ by substituting $x$ with $4$ in the function $f(x)$ . $\newline$ $f(4) = 2(4)^2 - 2(4) - 15$
Calculate $f(4)$ : Now, let's perform the calculations for $f(4)$ .
$f(4) = 2(16) - 8 - 15$
$f(4) = 32 - 8 - 15$
$f(4) = 24 - 15$
$f(4) = 9$
Find $g(f(4))$ : Next, we need to find the value of $g(f(4))$ by substituting $f(4)$ into $g(x)$ . Since we found $f(4) = 9$ , we will substitute $x$ with $9$ in the function $g(x)$ . $g(9) = 3(9) - 4$
Calculate $g(9)$ : Now, let's perform the calculations for $g(9)$ .
$g(9) = 3(9) - 4$
$g(9) = 27 - 4$
$g(9) = 23$
Final Answer: We have found the value of $g(f(4))$ , which is $g(9) = 23$ . $\newline$ This is the final answer.

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