Question

Given `g(x) = 5x^2 - 4x` and `h(x) =sqrt(x - 7)` how do you find g(h(x))?

Answer 1

`5x - 35 - 4sqrt(x-7)`

Explanation:

`g(h(x)) = g(sqrt(x-7))`

Now substitute x = `sqrt(x-7) " for x in g(x) "`

hence: `g(sqrt(x-7)) = 5(sqrt(x-7))^2 - 4(sqrt(x-7))`

now `(sqrt(x-7))^2 = x-7`

`rArr g(h(x)) = 5(x-7) -4(sqrt(x-7))`

`= 5x - 35 - 4(sqrt(x-7))`