Which function is the inverse of f(x)=log3x

Question

?(1 point)
Responses

f^−1(x)=3^log x
f^−1(x)=3^log x

f^−1(x)=x^3
f inverse of x is equal to x cubed

f^−1(x)=3^x
f inverse of x is equal to 3 to the x th power

f^−1(x)=3x

Answer 1

To find the inverse of the function $f(x)={\log }_{3}x$, we will follow these steps:

1. Replace $f(x)$ with $y$: $$y={\log }_{3}x$$

2. Swap $x$ and $y$ to find the inverse: $$x={\log }_{3}y$$

3. Solve for $y$: $$y=3^x$$

Thus, the inverse function is: $$f^{-1}(x)=3^x$$

Therefore, the correct response is: f^−1(x) = 3^x (f inverse of x is equal to 3 to the x th power).