Question

3. If f(x) = x² and g(x) = 3x - 1, find f(g(x))

Answer 1

f(g(x)) = 9x² - 6x + 1

Explanation:

We are told that:

•
`f(x) = x^2`

•
`g(x) = 3x -1`.

In order to find
`f(g(x))`, we have to replace
`x` in the definition of
`f(x)` with the definition of
`g(x)`. In other words,
`3x -1` has to be the input for
`f(x)`:

`f(g(x))` =
`f(3x -1)`

⇒
`(3x - 1)^2`

⇒
`9x^2 - 6x + 1`

Therefore, f(g(x)) = 9x² - 6x + 1.