Question

Given that f(x)= 4x-3 and g(x)= 2x-1 over 3 solve for g(f(2))

Answer 1

`g(f(2))=3`

Explanation:

So we have:

`f(x)=4x-3\text{ and } g(x)=(2x-1)/(3)`

And we want to solve for g(f(2)).

First, find f(2):

`f(2)=4(2)-3`

Multiply:

`f(2)=8-3`

Subtract:

`f(2)=5`

Now, substitute this in for g(f(2)):

`g(f(2))=g(5)`

Substitute this in for g(x):

`g(5)=(2(5)-1)/(3)`

Multiply:

`g(5)=(10-1)/(3)`

Subtract:

`g(5)=(9)/(3)`

Divide:

`g(5)=3`

Therefore:

`g(f(2))=3`