Question

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

Answer 1

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

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}`