Question
Find the inverse of the function f(x) = 5x4
.(1 point)
Responses
f−1(x) = 5x4
f−1(x) = 5x4
f−1(x) = 4x5
f−1(x) = 4x5
f−1(x) = 45x
f−1(x) = 45x
f−1(x) = 54x
f−1(x) = 54x
.(1 point)
Responses
f−1(x) = 5x4
f−1(x) = 5x4
f−1(x) = 4x5
f−1(x) = 4x5
f−1(x) = 45x
f−1(x) = 45x
f−1(x) = 54x
f−1(x) = 54x
Answers
GPT-4o mini
To find the inverse of the function \( f(x) = 5x^4 \), we need to follow these steps:
1. Replace \( f(x) \) with \( y \):
\[
y = 5x^4
\]
2. Swap \( x \) and \( y \):
\[
x = 5y^4
\]
3. Solve for \( y \):
\[
y^4 = \frac{x}{5}
\]
\[
y = \left( \frac{x}{5} \right)^{1/4}
\]
4. Therefore, the inverse function is:
\[
f^{-1}(x) = \left( \frac{x}{5} \right)^{1/4}
\]
None of the provided responses accurately reflect this inverse function.
If you need further assistance or clarification about finding inverses or other functions, feel free to ask!
1. Replace \( f(x) \) with \( y \):
\[
y = 5x^4
\]
2. Swap \( x \) and \( y \):
\[
x = 5y^4
\]
3. Solve for \( y \):
\[
y^4 = \frac{x}{5}
\]
\[
y = \left( \frac{x}{5} \right)^{1/4}
\]
4. Therefore, the inverse function is:
\[
f^{-1}(x) = \left( \frac{x}{5} \right)^{1/4}
\]
None of the provided responses accurately reflect this inverse function.
If you need further assistance or clarification about finding inverses or other functions, feel free to ask!