Let $$ f(x)=3 x+2 $$ and $$ g(x)=-2 x+1 $$ Find $$ g(f(-2)) $$

Question

UpStudy AI · Accepted Answer

To find $$ g(f(-2)) $$, we first need to calculate $$ f(-2) $$.

The function $$ f(x) $$ is defined as:
$$
f(x) = 3x + 2
$$

Substituting $$ -2 $$ into $$ f(x) $$:
$$
f(-2) = 3(-2) + 2 = -6 + 2 = -4
$$

Now that we have $$ f(-2) = -4 $$, we can find $$ g(f(-2)) = g(-4) $$.

The function $$ g(x) $$ is defined as:
$$
g(x) = -2x + 1
$$

Substituting $$ -4 $$ into $$ g(x) $$:
$$
g(-4) = -2(-4) + 1 = 8 + 1 = 9
$$

Thus, the final result is:
$$
g(f(-2)) = 9
$$

Therefore, the answer is $$ \boxed{9} $$.
$$ g(f(-2)) = 9 $$

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