Question

Let `f(x) = 7x^2+5` and g(x) = x-3, how do you find the composite function (f o g)(x)?

Answer 1

`f(g(x)) = 7x^2 - 42x + 68`

Explanation:

To find a composite function, you simply insert `g(x)` into `f(x)` anywhere you would find the `x` variable:
`f(g(x)) = 7(x-3)^2 +5`
`= 7(x^2 - 6x + 9) + 5`
`= 7x^2 - 42x + 63 + 5`
`= 7x^2 - 42x + 68`