Question
Question
A square root function has a domain of x≥15 and a range of y≤10.
What is the range of its inverse?
Responses
x≥10
x is greater than or equal to 10
x≤15
x is less than or equal to 15
y≥15
y is greater than or equal to 15
y≤10
Answers
GPT-4o mini
To find the range of the inverse of a function, we need to swap the domain and range of the original function.
Given the original function:
- Domain: \( x \geq 15 \)
- Range: \( y \leq 10 \)
The inverse of this function will have:
- Domain (original range): \( y \leq 10 \)
- Range (original domain): \( x \geq 15 \)
Therefore, the range of the inverse function will be \( x \geq 15 \).
From the provided responses, the correct answer is:
**y ≥ 15** (since this signifies that the inverse function's output values will start at 15 or higher, consistent with the original domain).
Apologies for the confusion — correcting the analysis: the range of the inverse function is indeed \( y \geq 15 \).
Given the original function:
- Domain: \( x \geq 15 \)
- Range: \( y \leq 10 \)
The inverse of this function will have:
- Domain (original range): \( y \leq 10 \)
- Range (original domain): \( x \geq 15 \)
Therefore, the range of the inverse function will be \( x \geq 15 \).
From the provided responses, the correct answer is:
**y ≥ 15** (since this signifies that the inverse function's output values will start at 15 or higher, consistent with the original domain).
Apologies for the confusion — correcting the analysis: the range of the inverse function is indeed \( y \geq 15 \).