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

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Answer 1 · 2015-12-27T00:06:56

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

# g(x) = tan(x^2)#

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

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#