Question

If `f(x)=e^(6x)`, `g(x)=2x+2` and `h(x)=sqrtx`, what is `f(g(h(x)))`?

Answer 1

`f(g(h(x)))=e^(12sqrtx+12)` or `e^12e^(6sqrtx)`

Explanation:

We have `f(x)=e^(6x)`, `g(x)=2x+2` and `h(x)=sqrtx`

hence `g(h(x))=g(sqrtx)=2sqrtx+2`

and `f(g(h(x)))=f(2sqrtx+2)`

= `e^(6(2sqrtx+2))`

= `e^(12sqrtx+12)`

= `e^12e^(6sqrtx)`