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(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!