Which function is the inverse of f(x)=log13 x ?(1 point) Responses f−1(x)=3x f superscript negative 1 baseline left parenthesis x right parenthesis equals 3 superscript x baseline f−1(x)=x3 f superscript negative 1 baseline left parenthesis x right parenthesis equals x superscript 3 baseline f−1(x)=x13 f superscript negative 1 baseline left parenthesis x right parenthesis equals x superscript Start Fraction 1 over 3 End Fraction baseline f−1(x)=(13)x f superscript negative 1 baseline left parenthesis x right parenthesis equals left parenthesis Start Fraction 1 over 3 End Fraction right parenthesis superscript x baseline

Answer 1

To find the inverse of the function \( f(x) = \log_{13} x \), we need to express it in a way that allows us to solve for \( x \) in terms of \( y \).

1. Start by rewriting the function with \( y \): \[ y = \log_{13} x \]

2. Now, we convert the logarithmic equation to an exponential one: \[ x = 13^y \]

This means the inverse function can be expressed as: \[ f^{-1}(x) = 13^x \]

From the given options, none of the answers precisely matches \( f^{-1}(x) = 13^x \).

However, the closest equivalent in the options is: \[ f^{-1}(x) = (13)^x \]

So the correct answer is: \[ f^{-1}(x) = (13)^x \]

Answer 2

Im sorry im not seeing that option sir