Question

Let ​f(x)=x2−4 and ​g(x)=7−x. Perform the composition or operation indicated. ​(fg)(8​)

Answer 1

Answer:

$(f\circ g)(8)=-3$

Step-by-step explanation:

Composite Function

Given f(x) and g(x) real functions, the composite function named $(f\circ g)(x)$ is defined as:

$(f\circ g)(x)=f(g(x))$

For practical purposes, it can be found by substituting g into f.

The functions are defined as follows:

$f(x)=x^2-4$

$g(x)=7-x$

To find $(f\circ g)(8)$, we evaluate g in x=8 and then apply the composition formula.

$g(8)=7-8=-1$

$(f\circ g)(8)=f(g(8))$

$(f\circ g)(8)=f(-1)$

$(f\circ g)(8)=(-1)^2-4=1-4$

$\boxed{(f\circ g)(8)=-3}$