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Problem presentation

This problem explores the composition of functions f(x), g(x), and h(x) to determine the values of x for which h(f(g(x))) equals 1/4. Given the functions f(x) = 4x, g(x) = x² + 1, and h(x) = 1/x, we start by rewriting each function in terms of y, where g(x) becomes y = x² + 1. Through substitution and manipulation, we find that h(f(g(x))) simplifies to 1/(4y). Setting this equal to 1/4 leads us to determine the relationship y = 1, ultimately yielding x = 0 as the solution.

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Problem presentation

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Presentation Transcript

  1. Problem presentation Meng Li 11/15/2012

  2. Problem set 2 • If f(x) = 4x, g(x) =x2+1, and h(x) =1/x, for what values of x is h(f(g(x))) =1/4?

  3. Solution • First we can rewrite all the equations: • Let g(x)=x2+1 =y then: • f(g(x))=f(y)=4y • h(f(g(x)))=h(4y)=1/(4y) • Since 1/(4y)=1/4, then: y=1 • So x2+1=1 • → We can get x=0

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