Questions: Given the definitions of (f(x)) and (g(x)) below, find the value of (f(g(2))). (f(x)=2 x^2+x-13) (g(x)=x-6)

Given the definitions of (f(x)) and (g(x)) below, find the value of (f(g(2))).

(f(x)=2 x^2+x-13)

(g(x)=x-6)
Transcript text: Given the definitions of $f(x)$ and $g(x)$ below, find the value of $f(g(2))$. \[ \begin{array}{l} f(x)=2 x^{2}+x-13 \\ g(x)=x-6 \end{array} \]
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Solution

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Solution Steps

Step 1: Evaluate \( g(2) \)

Given the function \( g(x) = x - 6 \), substitute \( x = 2 \) into the equation: \[ g(2) = 2 - 6 = -4 \]

Step 2: Evaluate \( f(g(2)) = f(-4) \)

Given the function \( f(x) = 2x^2 + x - 13 \), substitute \( x = -4 \) into the equation: \[ f(-4) = 2(-4)^2 + (-4) - 13 \] \[ f(-4) = 2(16) - 4 - 13 \] \[ f(-4) = 32 - 4 - 13 \] \[ f(-4) = 15 \]

Final Answer

\[ \boxed{f(g(2)) = 15} \]

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