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How do you find the compositions given #g(x) = x^2 + 2# and #f(x) = 2x#?

1 Answer

Dec 20, 2015

Compose the functions to find that

#(f@g)(x) = 2x^2#
and
#(g@f)(x) = 4x^2#

Explanation:

Composing functions is a simple as treating a function like a variable.

For #f(x) = 2x# and #g(x) = x^2# we have

#(f@g)(x) = f(g(x)) = f(x^2) = 2(x^2) = 2x^2#

and

#(g@f)(x) = g(f(x)) = g(2x) = (2x)^2 = 4x^2#

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