Question

If f(x)=4x+3 and g(x)=x^2-3 then f(g(2))

Answer 1

f(g(2))=7

Explanation:

The Composite Function

Given f(x) and g(x) as real functions, the composite function
`(f\circ g)(x)` is defined as:

`(f\circ g)(x)=f(g(x))`

It can be found by substituting g into f.

The given functions are:

`f(x)=4x+3`

`g(x)=x^2-3`

It's required to find f( g( 2 ) )

Find g(2):

`g(2)=2^2-3`

Operating:

`g(2)=4-3 =1`

g(2)=1

Now find f(1):

`f(1)=4(1)+3`

`f(1)=4+3 =7`

Thus:

f( g( 2 ) )=7