Question

If f(x) = x2 and g(x) = 4x + 3, find:
6) f(g(x))

Answer 1

The composition of f and g is given by

`f(g(x))=4x(4x+6)+9`

Explanation:

Given function f is defined by
`f(x)=x^(2)` and the

function g is defined by
`g(x)=4x+3`

Now to find the composition of f and g:

ie.,to find f(g(x)):

we know that
`(f \circ g)x=f(g(x))`

`f(g(x))=f(4x+3)`

`f(g(x))=(4x+3)^(2)`

`f(g(x))=(4x)^(2)+2(4x)(3)+(3)^(2)`

`f(g(x))=16x^(2)+24x+9`

`f(g(x))=4x(4x+6)+9`

Therefore
`f(g(x))=4x(4x+6)+9`

Therefore the composition of f and g is
`f(g(x))=4x(4x+6)+9`