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Please check pictureQuestionWhich of the following is a power function? Select all correct answers.Select all that apply:f(x)=6⋅16xf(x)=4x−−√9f(x)=10⋅3xf(x)=5⋅15x f(x)=−18x−−√3

Please check pictureQuestionWhich of the following is a power function Select all correct answersSelect all that applyfx616xfx4x9fx103xfx515x fx18x3 class=

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Answer:

The correct options are:

[tex]\begin{gathered} f(x)=4\sqrt[9]{x} \\ . \\ f(x)=-18\sqrt[3]{x} \end{gathered}[/tex]

Explanation:

A power function is a function that has the variable to the power of some fixed real number. A power function can't have the variable (x, in this problem) in the exponent.

Then, the only two option that follow this are:

[tex]\begin{gathered} f(x)=4\sqrt[9]{x} \\ . \\ f(x)=-18\sqrt[3]{x} \end{gathered}[/tex]

Because we can rewrite the exponent as:

[tex]\begin{gathered} f(x)=4\sqrt[9]{x}=4x^{\frac{1}{9}} \\ . \\ f(x)=-18\sqrt[3]{x}=-18x^{\frac{1}{3}} \end{gathered}[/tex]

Which is clearly, the variable to the power of a real number.

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