Question

F(x) =x+4/3 and g(x) = 3x – 4 Verify that the functions below are inverses by showing that (f o g)(x) = x and (g o f)(x) = x.

Answer 1

The answer is below

Explanation:

A composite function is a function which is placed inside another function, this type of function can be calculated by substituting one function into another function.

If two functions g(x) and f(x) are inverses, then each will reverse the effect of the other. That is, (f○g)(x)=f(g(x))=x and (g○f)(x)=g(f(x))=x.

Given that F(x) =(x+4)/3 and g(x) = 3x – 4

a) (f o g)(x) = f[g(x)]

= f(3x - 4)

= [(3x - 4) + 4]/3

= [3x - 4 + 4]/3

= 3x / 3

= 3

b) (g o f)(x) = g[f(x)]

= g[(x + 4)/3]

= 3(x + 4)/3 - 4

= x + 4 - 4

= x

We can see that (f o g)(x) = (g o f)(x) = x. Hence the functions are inverse functions.