Question

Which functions are equivalent to f (x) = RootIndex 4 StartRoot 162 EndRoot Superscript x? Check all that apply.

Answer 1

A.B. E.

Explanation:

Answer 2

`f(x)=162^(x)/(4)`

`f(x)=[3\sqrt[4]{2}]^(x)`

`f(x)=[3(2^{(1)/(4)})]^(x)`

Explanation:

we have

`f(x)=\sqrt[4]{162^(x)}`

Remember that

`\sqrt[n]{a^(m)}=a^(m/n)`

`(a^(m))^(n)=a^(m*n)`

so

1)
`\sqrt[4]{162^(x)}=162^(x)/(4)`

2) The number 162 decompose in prime factors is

`162=(2)(3^4)`

substitute

`f(x)=\sqrt[4]{[(2)(3^4)]^(x)}={[(2)(3^4)]^(x/4)={{[(2)(3^4)]^((1/4))}^x=[3\sqrt[4]{2}]^(x)`

3)
`f(x)=[3\sqrt[4]{2}]^(x)=[3(2^{(1)/(4)})]^(x)`

therefore

`f(x)=162^(x)/(4)`

`f(x)=[3\sqrt[4]{2}]^(x)`

`f(x)=[3(2^{(1)/(4)})]^(x)`