?(1 point)
Responses
f^−1(x)=x^3
f superscript negative 1 baseline left parenthesis x right parenthesis equals x superscript 3 baseline
f^−1(x)=x^1/3
f superscript negative 1 baseline left parenthesis x right parenthesis equals x superscript Start Fraction 1 over 3 End Fraction baseline
f^−1(x)=(1/3)^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)=3^x
1 answer
To find the inverse of the function \( f(x) = \log_{1/3} x \), we need to express \( x \) in terms of \( y \), where \( y = f(x) \).
We start with the equation:
\[
y = \log_{1/3} x
\]
By the definition of logarithms, we can rewrite this in exponential form:
\[
x = (1/3)^y
\]
To find the inverse function, we solve for \( y \) in terms of \( x \):
\[
f^{-1}(x) = 3^x
\]
Thus, the inverse function is: \[ \boxed{f^{-1}(x) = 3^x} \]
