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

Question

?(1 point)
Responses

f−1(x)=x3
f superscript negative 1 baseline left parenthesis x right parenthesis equals x cubed

f−1(x)=3x
f superscript negative 1 baseline left parenthesis x right parenthesis equals 3 superscript x baseline

f−1(x)=3x
f superscript negative 1 baseline left parenthesis x right parenthesis equals 3 x

f−1(x)=3logx

Answer 1

To find the inverse of the function \( f(x) = \log_3(x) \), we can follow these steps:

1. Replace \( f(x) \) with \( y \): \[ y = \log_3(x) \]

2. Switch \( x \) and \( y \): \[ x = \log_3(y) \]

3. Convert the logarithmic equation to its exponential form: \[ y = 3^x \]

So, the inverse function is: \[ f^{-1}(x) = 3^x \]

Therefore, the correct option, which states the inverse function, is: \[ f^{-1}(x) = 3^x \]