Question

The function
f
(
x
)
is graphed in the first quadrant.



image.png

The inverse function
f
−
1
(
x
)
can be formed if the domain of
f
(
x
)
is restricted. Which of the options best defines this restricted domain?


0
≤
x
≤
3.6


1
≤
x
≤
10


1
≤
x
≤
7.5


3.6
≤
x
≤
10

Answer 1

I can’t see the graph you attached. Could you re-upload the image or describe the graph (where it increases/decreases and any turning points or labeled points like x = 3.6, 7.5, 10, 1)?

How to decide (so you can check quickly):

- An inverse exists only if f is one-to-one on the restricted domain — equivalently, f must be monotonic (always increasing or always decreasing) on that interval.
- Find any x where f has a local maximum or minimum (a turning point). Your restricted interval must not include that turning point.
- From the four choices, pick the interval that lies entirely on one monotonic side of the turning point.

If you upload the graph or describe it (e.g., “f rises from x=0 to x=3.6 then falls from 3.6 to 10”), I’ll pick the correct option.