Math  /  Algebra

QuestionFor the following exercises, find functions f(x)f(x) and g(x)g(x) so the given function can be expressed as h(x)=f(g(x))h(x)=f(g(x))
26. h(x)=(x+2)2h(x)=(x+2)^{2}
27. h(x)=(x5)3h(x)=(x-5)^{3}
28. h(x)=3x5h(x)=\frac{3}{x-5}
29. h(x)=4(x+2)2h(x)=\frac{4}{(x+2)^{2}}
30. h(x)=4+x3h(x)=4+\sqrt[3]{x}
31. h(x)=12x33h(x)=\sqrt[3]{\frac{1}{2 x-3}}
32. h(x)=1(3x24)3h(x)=\frac{1}{\left(3 x^{2}-4\right)^{-3}}
33. h(x)=3x2x+54h(x)=\sqrt[4]{\frac{3 x-2}{x+5}}

Studdy Solution
Verify that f(g(x))=h(x)f(g(x)) = h(x). f(g(x))=f(3x2x+5)=3x2x+54=h(x) f(g(x)) = f\left(\frac{3x-2}{x+5}\right) = \sqrt[4]{\frac{3x-2}{x+5}} = h(x)

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