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Question 519189: Let f(x) = 2x - 4 and g(x) = 0.5x+2.
Find f(g(x))
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! What does f(g(x)) mean? It means that you are to find f(x) when x is g(x). So all that this problem is asking you to do is to take the f(x) equation and replace any x in it with g(x).
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So start with f(x) = 2x - 4
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Then replace the x in f(x) with g(x), or to be more specific, on the left side of the f(x) equation, replace the x with g(x) and then on the right side of the f(x) equation replace any x with (0.5x + 2) which is the right side of the g(x)equation.
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When you do that the left side gets written as f(g(x)) and the right side in which the x gets replaced with g(x) gets written as shown:
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f(g(x)) = 2(0.5x + 2) - 4
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Then simplify the right side by doing the distributed multiplication (multiply 2 times each of the terms in the parentheses) and you have:
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f(g(x)) = 2*0.5x + 2*2 - 4 = x + 4 - 4
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Note that the +4 and the -4 cancel and you are left with just:
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f(g(x)) = x
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That's the answer you were to get.
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Hopefully from this you have learned that f(g(x)) tells you to start with the right side of the f(x) equation and everywhere that you see an x you replace it with the right side of the equation for g(x) and then simplify it.
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