Question

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if $f(x)=x^{2}-4x - 6$ and $g(x)=-3x$, find the following composition.
$(f\circ g)(-4)$

$(f\circ g)(-4)=\square$

Explanation:

Step1: Find g(-4)

To find \( (f \circ g)(-4) \), we first need to find \( g(-4) \). The function \( g(x) = -3x \), so substitute \( x = -4 \) into \( g(x) \):
\( g(-4) = -3 \times (-4) = 12 \)

Step2: Find f(g(-4)) = f(12)

Now, we substitute the result of \( g(-4) \) (which is 12) into the function \( f(x) \). The function \( f(x) = x^2 - 4x - 6 \), so substitute \( x = 12 \):
\( f(12) = 12^2 - 4 \times 12 - 6 \)
First, calculate \( 12^2 = 144 \), \( 4 \times 12 = 48 \). Then:
\( f(12) = 144 - 48 - 6 \)
\( f(12) = 96 - 6 = 90 \)

Answer:

90