How do you write l(x) = (tan(x^2))^.5 as a composition of two or more functions?

1 Answer
Dec 27, 2015

l(x) = f(g(x)) = (tan(x^2))^(1/2)

g(x) = tan(x^2)

f(x) = x^(1/2) = x^(.5)

Explanation:

There are multiple way to answer this question but the most simple (in my opinion) is this

We know l(x) = (tan(x^2))^(1/2)

We also know that l(x) = f(g(x)) (definition of composition of function)

We can let the inside function be
g(x) = tanx^2

And the outside function f(x) = x^(1/2) = sqrtx

l(x) = f(g(x)) = f(tanx^2) = (tan(x^2))^(1/2) = (tan(x^2))^.5