Asked by Martha Lucia on May 12, 2024
Verified
Use the horizontal Line Test to determine if the function is one-to-one and so has an inverse function.
f(x) =81−x2f ( x ) = \sqrt { 81 - x ^ { 2 } }f(x) =81−x2
A) f is one-to-one
B) f is not one-to-one
C) cannot be determined
Horizontal Line Test
A method used to determine if a function is injective or one-to-one, based on whether any horizontal line intersects the graph more than once.
One-to-One
A function for which every element of the range of the function corresponds to exactly one element of the domain.
- Apply the horizontal line test to determine if a function is one-to-one and whether it has an inverse.
Verified Answer
MS
Michelle SalasMay 13, 2024
Final Answer :
B
Explanation :
If we take any value of x between -9 and 9, we get a unique value of f(x). However, if we take any value of x beyond -9 to 9, we get two values of f(x). This means that there are multiple inputs that lead to the same output, and hence f is not one-to-one. Therefore, it does not have an inverse function.
Learning Objectives
- Apply the horizontal line test to determine if a function is one-to-one and whether it has an inverse.