Given g(x)=4x^2+3 and f(x)=3x-1, solve f(g(x))?

Question

Given g(x)=4x^2+3 and f(x)=3x-1, solve f(g(x))?

Answer 1

substitute the equation g(x) into f(x) for x.

=3(g(x))-1

=3(4x^2+3)-1

=12x^2+9-1

=12x^2+8

Answer 2

g(x)=4x^2+3 and f(x)=3x-1

f[g(x) = 3(4x^2+3) -1

= 12x^2 +9 -1

= 12x^2 +8

= 4(3x^2 +2)

Answer 3

12x^2+8=f(g(x))

Answer 4

This is called composition of functions.

Think of it this way...

If you see f(5), I hope you know that that means you are going to insert a 5 wherever you have an x.

For your problem f(5) you would have 3*(5) - 1.

It's the same logic with composition.  Instead of a 5 we're going to put the entire g(x) in where we have an x in f ( x).

So if f(x) = 3x - 1 and g(x) = 4x^2 + 3 then f(g(x)) is:

3*(4x^2 + 3) - 1

Distribute the 3

12x^2 +9 - 1

Simplify

f(g(x)) = 12x^2 + 8

Hope this helped