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).