Question

Composite Function: For f(x)=2x+3 and g(x)=−x²+1, find the composite function defined by (f∘g)(x).

A) 2x²+3
B) −2x²+7
C) −2x²−3
D) 2x²−5

Answer 1

To find the composite function (f∘g)(x), substitute g(x) into f(x): f(g(x)) = f(−x²+1) = − 2x² + 5, thus the composite function is − 2x² + 5.

Step-by-step explanation:

To find the composite function (f∘g)(x), we need to substitute the function g(x) into the function f(x). Given f(x)=2x+3 and g(x)=−x²+1, the composition (f∘g)(x) is calculated as f(g(x)).

Let's substitute g(x) into f(x):

Thus, the composite function (f∘g)(x) is − 2x² + 5.