Let f(x) = square root of x , g(x) = x^2 − 1, and h(x) = 1/x . Find (f ∘ g ∘ h)(x

Answer 1

Finding f[g[h(x)]];

Put h into the g function gives:

g(1/x ) = (1/x)²-1.

Now put that result into the f function.

f( (1/x)²-1 ) = √( (1/x)²-1).

That can be simplified a bit if you want to:

√((1/x²)- (x²/x²)) = √(1-x²)/√x²= √(1-x²)/|x|

Here is a graph to help picture what the domain of the composite function looks like:

desmos.com/calculator/dv4symkefy

Answer 2

g(h(x)) = (1/x)² - 1 = 1/x² - 1

f(g(h(x))) = √(1/x² - 1)

Answer 3