Question

Perform the requested operation or operations. f(x) = x minus five divided by eight.; g(x) = 8x + 5, find g(f(x))

Answer 1

g(f(x))=x.

Explanation:

Given :f(x)=
`(x-5)/(8)` and g(x)=8x+5.

g(f(x)) = g(
`(x-5)/(8)`) (Substituting f(x) value)

=
`8((x-5))/(8) +5` (Replacing x by
`(x-5)/(8)`)

=x-5+5 (Simplifying)

=x.

g(f(x))=x.

Answer 2

Given:
f(x) = (x - 5)/8
g(x) = 8x + 5

Therefore

`g(f(x))\\=8( (x-5)/(8))+5\\=x-5+5\\=x`
This means that g(x) is the inverse of f(x) and vice versa.

Answer: g(f(x)) = x