the function f(x) is invertible on the intervals:
B: -7 ≤ x ≤ -4
C : 1 ≤ x ≤ 3
In which intervals is the function invertible?
A function f(x) can only be invertible if it is one-to-one in its domain, where one-to-one means that each output is related to only one input.
So, if for two different values x₁ and x₂ we have that:
f(x₁) = f(x₂) = y, then the function is not invertible.
So here what we need to do is identify in which interval is the function one-to-one.
If you look at the last option, we have the interval [1, 3]
We have that f(1) = 2, and then the function increases until f(3) = 4
In that interval the function is cleraly one-to-one, so, on that interval, we can find an inverse function to f(x).
Similarly, on the second option [-7, -4] we also can see that:
f(-7) = 2
And then the function increases until f(-4) = 4
Then the function is also invertible on that interval.
We conclude that the function f(x) is invertible on the intervals:
B: -7 ≤ x ≤ -4
C : 1 ≤ x ≤ 3
If you want to learn more about invertible functions:
https://brainly.com/question/14391067
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