Find f(x) and g(x)

Question

If (f•g)(x) = 2x-1 how might f(x) and g(x) be defined?

A) f(x)= (x-1) and g(x)=(2x-1)

B) f(x)= (x-1) and g(x)=(2x+1)

C) f(x)= (2x-1) and g(x)=(x-1)

D) f(x)= (2x+1) and g(x)=(x-1)

Answer 1

For this beautiful problem , we have to make sure that your are familiar with the composite function.

(f.g) (x)= The dot between the letters f and g means composite function , doesn't mean product. You can write this function as f(g(x)), where you have to substitute the g(x) function into f(x) function to obtain a composite function.

Let proof that (f.g) (x)= 2x-1

Let select the following :

f(x) = 2x+1. and g(x) =x-1.

2) I am going to substitute g(x) into f(x). meaning whatever value of g(x) will be replaced by x in the f(x) or the outside function.

The inside function g(x),will be replace in the outside function f(x) as follow :

(f.g) (x) = f (g(x) = 2x-1 = 2 (x-1) +1 distributive property = 2x-2+1 = 2x-1

3) (f.g)(x) =2x-1 That is your answer or D.