Can anyone explain how to answer these types of questions? I don't get how this person got A (which was correct). Thank you, any and all clarification is appreciated!
![Can anyone explain how to answer these types of questions I dont get how this person got A which was correct Thank you any and all clarification is appreciated class=](https://us-static.z-dn.net/files/d1a/d601cc3934120ad647b4ac15b0b074ee.jpg)
Answer:
C) [-2, 7]
Step-by-step explanation:
The domain of a function is the set of all possible input values (x-values) for which the function is defined.
The graph shows a continuous curve f(x) with closed circle endpoints at x = -6 and x = 10. The closed circles indicate that those values of x are included in the domain. Therefore, the domain of the graphed function f(x) is [-6, 10].
[tex]\dotfill[/tex]
The range of a function is the set of all possible output values (y-values) for which the function is defined.
The minimum y-value of the curve is y = -2 and the maximum y-value is y = 7. As both these values are included in the range, the range of the graphed function f(x) is [-2, 7].
[tex]\dotfill[/tex]
An inverse function essentially reverses the operation done by a given function. For a function to have an inverse, it must be bijective, meaning each output is associated with exactly one input, and every possible output is achieved by some input.
Graphically, the inverse function is a reflection of the original function across the line y = x. Therefore:
In this case, the graphed function f(x) is bijective, so it has an inverse f⁻¹(x). Therefore:
So, the domain of f⁻¹(x) is:
[tex]\Large\boxed{\boxed{\textsf{Domain of $f^{-1}(x)$}=[-2, 7]}}[/tex]
1. Domain of f(x):
Note:
2. Range of f(x):
Note:
Based on the given options, the closest interval to the domain of [tex]f^{-1}(x)[/tex] is:
[tex]\boxed{[-2,7].}[/tex]