Find the function f and g so that f of g =h

Question

H(x)=square root 1-x^2

Answer 1

H(x) = √(1-x²)

 

We want H(x) = f(g(x))

 

g(x) is the "inside" function and f(x) is the "outside" function

 

For √(1-x²), the "inside" function is 1-x² and the "outside" is the square root function.

 

So, if f(x) = √x and g(x) = 1-x², then f(g(x)) = f(1-x²) = √(1-x²) = H(x)