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Question 885930: Hi, I am needing help with my functions homework. I'd really appreciate any assistance.
For certain pairs of functions f and g. (f o g)(x)=x and (g o f)(x)=x. Show that this is true for each pair of exercises below:
1. f(x)=4x+2, g(x)= 1/4(x-2)
Also help with this one:
Find functions f and g such that (f o g)(x)=h(x)
1. h(x)=(6x-2)^2
2. h(x)= √6x +12
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! 1. f(x)=4x+2, g(x)= (1/4) * (x-2)
(f o g)(x) = f(g(x)) = 4(1/4(x-2) + 2 = x-2 +2 = x
(g o f)(x) = g(f(x)) = 1/4 * (4x+2-2) = 4x/4 = x
2.1) h(x)=(6x-2)^2
f(x) = x^2, g(x) = (6x-2)
(f o g)(x) = f(g(x)) = f(6x-2) = (6x-2)^2 = h(x)
2.2) h(x)= √6x +12
f(x) = √x +12, g(x) = 6x
(f o g)(x) = f(g(x)) = f(6x) = √6x +12 = h(x)
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