If f(x)=3x-2 and g(x)=(1)/(3)x+1, then (f(g))^(-1) (x) equals: a. 1-x b. x-1 c. (1)/(3) (3x-1) d. x+1

Question

If
`f(x)=3x-2` and
`g(x)=(1)/(3)x+1`, then
`(f(g))^(-1) (x)` equals:

a.
`1-x`
b.
`x-1`
c.
`(1)/(3) (3x-1)`
d.
`x+1`

Answer 1

• B) x - 1

=================

Given

• f(x) = 3x - 2, g(x) = 1/3x + 1

Find the composite function f(g(x))

• f(g(x)) = 3(1/3x +1) - 2 = x + 3 - 2 = x + 1

Find the inverse of f(g(x))

• x = f(g)⁻¹(x) + 1
• f(g)⁻¹(x) = x - 1

Correct choice is B