Question

Which function is the inverse of f(x)=log3x
?(1 point)
Responses

f−1(x)=3x
f inverse of x is equal to 3 to the x th power

f−1(x)=3logx
f−1(x)=3logx

f−1(x)=x3
f inverse of x is equal to x cubed

f−1(x)=3x

Answer 1

To find the inverse of the function \( f(x) = \log_3(x) \), we need to switch the roles of \( x \) and \( y \) and then solve for \( y \).

1. Start with the original function:
\[
y = \log_3(x)
\]

2. Swap \( x \) and \( y \):
\[
x = \log_3(y)
\]

3. Rewrite this in exponential form:
\[
y = 3^x
\]

Thus, the inverse function is:
\[
f^{-1}(x) = 3^x
\]

So, the correct response is:
**f−1(x)=3^x (f inverse of x is equal to 3 to the x th power).**