Question

Let `f(x)=1-x` and `g(x)= x^2` and `h(x)= 1/x`, how do you find f(h(g(x)))?

Answer 1

You apply each of the functions in order, starting from the innermost parentheses. In this case, `f(h(g(x)))= 1 - 1/x^2`.

Explanation:

`f(x)=1-x`
`g(x)=x^2`
`h(x)=1/x`

To find `f(h(g(x)))` we start from the innermost bracket, and then apply each function to what we have 'so far' as though it were the `x` value in that function.

So, starting from the innermost parentheses, we have `g(x)=x^2`. We don't do anything else with that at this stage, but now we are going to find `h(g(x))`.

`h(x)=1/x`, but in this case we let `g(x)`, which is `x^2`, stand in for the `x` in this expression, so we end up with `h(g(x))=1/x^2`.

The next step is to find `f(h(g(x)))`, our answer. `f(x)=1-x` but we let `h(g(x))=1/x^2` stand in for `x`, so we end up with `f(h(g(x)))= 1 - 1/x^2`