Question

If f(x)=x^4+4, g(x)=x-1 and h(x)=x, then f(g(h(x)))=?

This is compound and inverse functions.

Answer 1

`f(x)=x^4+4` `color(white)(wwwww` `g(x)=x-1` `color(white)(wwwww` `h(x)=x`

We need to find, `f(g(h(x)))`

`=> f(g(x))` `color(white)(wwwowwwww` `["as "h(x)=x]`

`=> f(x-1)` `color(white)(wwwwwwww` `["as "g(x)=x-1]`

`=> (x-1)^4 +4` `color(white)(wwowww` `["as "f(x)=x^4+4]`