Question
Consider the exponential function g(x)=5^x
Determine which function is the inverse of g(x).
(2 points)
Responses
g−1(x)=15x
g inverse of x is equal to the fraction with numerator 1 and denominator 5 to the x th power
g−1(x)=−5x
g inverse of x is equal to negative 5 to the x th power
g−1(x)=5logx
g−1(x)=5logx
g−1(x)=log5x
g inverse of x is equal to the log base 5 of x
Determine which function is the inverse of g(x).
(2 points)
Responses
g−1(x)=15x
g inverse of x is equal to the fraction with numerator 1 and denominator 5 to the x th power
g−1(x)=−5x
g inverse of x is equal to negative 5 to the x th power
g−1(x)=5logx
g−1(x)=5logx
g−1(x)=log5x
g inverse of x is equal to the log base 5 of x
Answers
GPT-4o mini
To find the inverse of the function \( g(x) = 5^x \), we need to express \( x \) in terms of \( y \), where \( y = g(x) \).
1. Start with the equation:
\[
y = 5^x
\]
2. To find the inverse, we solve for \( x \):
\[
x = \log_5(y)
\]
3. Thus, the inverse function can be written as:
\[
g^{-1}(x) = \log_5(x)
\]
Given this, the correct response from your options is:
\( g^{-1}(x) = \log_5(x) \) (g inverse of x is equal to the log base 5 of x).
1. Start with the equation:
\[
y = 5^x
\]
2. To find the inverse, we solve for \( x \):
\[
x = \log_5(y)
\]
3. Thus, the inverse function can be written as:
\[
g^{-1}(x) = \log_5(x)
\]
Given this, the correct response from your options is:
\( g^{-1}(x) = \log_5(x) \) (g inverse of x is equal to the log base 5 of x).