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Use the functions below.

f(x)=x2−6
g(x)=−x3
What is (f∘g)(−2)
?

(1 point)
Responses

(f∘g)(−2)=−27,000
open paren f circ g close paren times negative 2 is equal to negative 27 comma 000

(f∘g)(−2)=58
open paren f circ g close paren times negative 2 is equal to 58

(f∘g)(−1)=38
open paren f circ g close paren times negative 1 is equal to 38

(f∘g)(−2)=8

1 answer

To find \((f \circ g)(-2)\), we first need to evaluate \(g(-2)\) and then apply the result to the function \(f\).

  1. Calculate \(g(-2)\): \[ g(x) = -x^3 \] So, \[ g(-2) = -(-2)^3 = -(-8) = 8 \]

  2. Now, apply \(f\) to the result from \(g\): \[ f(x) = x^2 - 6 \] Therefore, \[ f(g(-2)) = f(8) = 8^2 - 6 = 64 - 6 = 58 \]

Thus, \((f \circ g)(-2) = 58\).

The correct response is: \[ \text{(f∘g)(−2)=58} \]