Question
Which function is the inverse of f(x)=log13 x
?(1 point)
Responses
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
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
?(1 point)
Responses
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
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
Answers
GPT-4o mini
To find the inverse of the function \( f(x) = \log_{13}(x) \), we first need to understand that the inverse of a logarithmic function is an exponential function. Specifically, if \( y = \log_{b}(x) \), then the inverse is \( x = b^{y} \).
1. Start with \( y = \log_{13}(x) \).
2. Rewrite in exponential form: \( x = 13^{y} \).
3. Switch \( x \) and \( y \) to find the inverse: \( y = 13^{x} \).
Thus, the inverse function is \( f^{-1}(x) = 13^{x} \).
Therefore, the correct answer is:
**\( f^{-1}(x) = 13^{x} \)**
1. Start with \( y = \log_{13}(x) \).
2. Rewrite in exponential form: \( x = 13^{y} \).
3. Switch \( x \) and \( y \) to find the inverse: \( y = 13^{x} \).
Thus, the inverse function is \( f^{-1}(x) = 13^{x} \).
Therefore, the correct answer is:
**\( f^{-1}(x) = 13^{x} \)**