Question

Given f(x) = x² + 8x and g(x) = x4, choose
the expression for (fºg)(x).

Answer 1

Answer: fg(x) = 16x² + 32x

Method:
First you must substitute g(x) into f(x).
Where the x is in the equation f(x) substitute the equation of g(x).
So it should be fg(x) = (x4)²+ 8(x4).
Then simplify the equation to
fg(x) = 16x² + 32x

Answer 2

The expression for the new function (fog(x)) = x⁸ + 8x⁴

What is a composite function?

A composite function some called function of a function is a process whereby two functions produce a third function.

Let assume there is a function f(x) and g(x), a composite function fog(x) read as f of g of x, produces a third function h(x).

In the given question, we are to find (fog) (x), we will replace the value of the function g(x) for x in f(x).

i.e.

f(g(x) = x² + 8x

`f(g(x) = (x^4)^2+8(x^4)`

`f(g(x)) = x^8+8x^4`