Question

How do you write the combined function as a composition of several functions if `f(g(x)) = sqrt (1-x^2) +2`?

Answer 1

If I remember correctly there are many "right" ways to solve this equation. `f(g(x))` merely means you are plugging a function of `x` into `g` into `f` with each letter being a different function.

For instance: your equation for `g` could possibly be `sqrt(1-x^2)`.
After, we plug in `x` into that equation we get the same function (`sqrt(1-x^2)`).

Next step when solving multiple step functions is to plug in your result of your first function (in our case `g`) into the new function (`f`). This is where we need another function to get `sqrt(1-x^2)` into `sqrt(1-x^2)` `+2`.

For this step we may say `(f)= x+2`.

When we plug in `sqrt(1-x^2)` into our new `(f)=x+2` our result is
`sqrt(1-x^2)` `+2`, the equation we needed to get to.

Another solution would be to have `(g)= 1-x^2` and `(f)=sqrt(x)+2`
There are many more solution, just be creative, these are only two!