Question

If f(x)=x-3/x, g(x)=x+3, and h(x)=2x+1, what is (g*h*f)(x).

A. 3x-6/x
B. 6x-6/x
C. 2x+4/2x+7
D. 4x-3/x

Answer 1

Answer = (g*h*f)(x) = 4x-3/x

Answer 2

Option B - 6x-6/x

Explanation:

Given : If
`f(x)=(x-3)/(x), g(x)=x+3,h(x)=2x+1`.

To find : What is the value of
`(g(h(f)))(x)`

Solution :

`(g(h(f)))(x)=g(h(f(x)))`

i.e, substitute the value of f(x) in h(x) and then put that h(x) in g(x).

`g(h(f(x)))=g(h((x-3)/(x)))`

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

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

Solving the RHS,

`=(2((x-3)/(x))+1)+3`

`=((2x-6)/(x))+1)+3`

`=((2x-6+x)/(x))+3`

`=(3x-6)/(x)+3`

`=(3x-6+3x)/(x)`

`=(6x-6)/(x)`

Therefore, The value of
`(g(h(f)))(x)=(6x-6)/(x)`

Hence, Option B is correct.