Question
Which function is the inverse of f(x)=log
3
1
x?
A. f
−1
(x)=x
3
B. f
−1
(x)=3
x
C. f
−1
(x)=(
3
1
)
x
D. f
−1
(x)=x
3
1
3
1
x?
A. f
−1
(x)=x
3
B. f
−1
(x)=3
x
C. f
−1
(x)=(
3
1
)
x
D. f
−1
(x)=x
3
1
Answers
GPT-4o mini
To find the inverse of the function \( f(x) = \log_3 (x) \), we need to switch the roles of \( x \) and \( y \) and solve for \( y \).
1. Start with the equation:
\[
y = \log_3 (x)
\]
2. Rewrite it in exponential form:
\[
x = 3^y
\]
3. Now, solve for \( y \):
\[
y = 3^x
\]
So the inverse function is:
\[
f^{-1}(x) = 3^x
\]
Thus, the correct answer is:
**B. \( f^{-1}(x) = 3^x \)**.
1. Start with the equation:
\[
y = \log_3 (x)
\]
2. Rewrite it in exponential form:
\[
x = 3^y
\]
3. Now, solve for \( y \):
\[
y = 3^x
\]
So the inverse function is:
\[
f^{-1}(x) = 3^x
\]
Thus, the correct answer is:
**B. \( f^{-1}(x) = 3^x \)**.