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Stells [14]
4 years ago
9

Given f(x), find g(x) and h(x) such that f(x)=g(h(x)) and neither g(x) nor h(x) is solely x. f(x)=−3x+4⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√3+5

Mathematics
1 answer:
iVinArrow [24]4 years ago
7 0

Answer:

h(x)=-2x+4

g(x)=\sqrt[3]{x}-5

Step-by-step explanation:

Consider the given function is

f(x)=\sqrt[3]{-2x+4}-5

It is given that f(x)=g(h(x)) and neither g(x) nor h(x) is solely x.

f(x)=\sqrt[3]{(-2x+4)}-5

Let h(x)=-2x+4, then we get

f(x)=g(h(x))=\sqrt[3]{h(x)}-5

Substitute h(x)=x in the above function.

g(x)=\sqrt[3]{x}-5

Therefore, the required functions are h(x)=-2x+4 and g(x)=\sqrt[3]{x}-5.

Check the solutions.

g(h(x))=g(-2x+4)             [\because h(x)=-2x+4]

g(h(x))=\sqrt[3]{-2x+4}-5            [\because g(x)=\sqrt[3]{x}-5]

g(h(x))=f(x)

Therefore, our solution is correct.

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<u>Step-by-step explanation:</u>

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Use Long division, Synthetic division, or plug them into the equation to see which root(s) work <em>(result in a remainder of zero)</em>.

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1 |  1    2    -5     -6

  |<u>  ↓    1      3     -2 </u>      

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