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

##### 1 Answer
Feb 1, 2016

If I remember correctly there are many "right" ways to solve this equation. $f \left(g \left(x\right)\right)$ 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 $\left(f\right) = x + 2$.

When we plug in $\sqrt{1 - {x}^{2}}$ into our new $\left(f\right) = x + 2$ our result is
$\sqrt{1 - {x}^{2}}$$+ 2$, the equation we needed to get to.

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