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Question 191326: I just learned Composite functions last class and I am really struggling with it... Is there any way you can show me how to do this with steps so that I can see exactly how this is done please.
Let f(x)=x/x-1, g(x)=-4/x, and h(x)=3x-2
Find the domain of f
Find the domain of g
Find the domain of h
Find (fog)(x)
Find the domain of fog
Find (fog)(2)
Find (goh)(x)
Find the slope of h(x)
Determine whether h(x) is an increasing, decreasing or constant function
Find h^-1(x)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Let f(x)=x/x-1,
g(x)=-4/x,
and h(x)=3x-2
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Find the domain of f: all Real numbers except x = 1
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Find the domain of g: all Real numbers except x = 0
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Find the domain of h: all Real numbers
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Find (fog)(x) =f[-4/x) = (-4/x)/(-4/x)-1) = (-4/x)/[(-4-x)/x]
= [4(4+x)] = 16+4x
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Find the domain of fog: all Real Numbers
Find (fog)(2) = f(g(2)) = f(-4/2) = = f(-2) = -2/(-2-1) = 2/3
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Find (goh)(x) = g[3x-2] = -4/(3x-2)
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Find the slope of h(x): slope = 3
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Determine whether h(x) is an increasing, decreasing or constant function
Increasing because the slope is greater than 3
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Find h^-1(x) = (x+2)/3
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Cheers,
Stan H.
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