How do you find the compositions given #f(x) = |x - 2#|, #g(x) = sqrtx#?

1 Answer
KillerBunny
Jul 5, 2018

#f(g(x))=f(sqrt(x))=|sqrt(x)-2|# and #g(f(x))=g(|x-2|)=sqrt(|x-2|)#

Explanation:

Every function has an input and an output. Composing two functions means to use the output of the first as the input for the second.

So, #f(x)# takes an input #x# and outputs the absolute value of the input minus two.
#g(x)# takes an input #x# and ouputs the square root of the input.

So, #f(g(x))=f(sqrt(x))=|sqrt(x)-2|# and #g(f(x))=g(|x-2|)=sqrt(|x-2|)#

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