Fcn-comp. Q: if h(x) = x(sqrt(1-x)), f(y) = sqrt(y), and h(x) = f(g(x)), what is g(x)

[kaanj]

Hello! The function h(x) = x(sqrt(1-x)) can be thought of as a function composition h(x) = f(g(x)).

What is g(x) if f(y) = sqrt(y)?

How should I approach this problem?

 

[Otis]

Hello! The function h(x) = x(sqrt(1-x)) can be thought of as a function composition h(x) = f(g(x)).

What is g(x) if f(y) = sqrt(y)?

How should I approach this problem?

You defined: h(x) = x * sqrt(1-x)

Did they give you the domain for function h? Without a domain statement, I'm thinking that function h ought to include absolute-value symbols.

h(x) = |x| * sqrt(1-x)

:-?

 

[pka]

Hello! The function h(x) = x(sqrt(1-x)) can be thought of as a function composition h(x) = f(g(x)).
What is g(x) if f(y) = sqrt(y)?

The answer to that exact question is \(\displaystyle g(x)=\begin{cases} x^2(1-x) &\: 0 \le x\le 1\\x^2(1-x) &\: x <0\\\text{not defined} &\: \text{else}\end{cases}\)