Which function is the inverse of f(x)=log1/3 x

Question

?(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

Answer 1

To find the inverse of the function $f(x)={\log }_{1/3}x$, we need to express $x$ in terms of $y$, where $y=f(x)$.

1. We start with the equation:
   $$y={\log }_{1/3}x$$

2. By the definition of logarithms, we can rewrite this in exponential form:
   $$x=(1/3{)}^y$$

3. To find the inverse function, we solve for $y$ in terms of $x$:
   $$f^{-1}(x)=3^x$$

Thus, the inverse function is: $$\boxed{{\displaystyle f^{-1}(x)=3^x}}$$