Question

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

Answer 1

The correct options are:

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

Step-by-step 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:

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

Because we can rewrite the exponent as:

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

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