If #h(x)=(f-g)(x), f(x)=5x+2# how do you determine g(x) given #h(x)=sqrt(x-4)+5x+2#?

1 Answer
lechugamaestro19
Feb 27, 2018

#g(x) = -sqrt(x-4)#

Explanation:

Firstly, it's important to note that #(f-g)(x)# is the same thing as #f(x) - g(x)#.

#h(x) = f(x) - g(x)#

We can substitute the function names out for the actual functions to find our answer.

#sqrt(x-4) + 5x + 2 = 5x + 2 - g(x)#
#sqrt(x-4) + cancel(5x + 2) = cancel(5x + 2) - g(x)#
#sqrt(x-4) = -g(x)#

#g(x) = -sqrt(x-4)#

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