Answer:
B. The value is between 1 and 2
Explanation:
Im kinda unsure about this one because I haven't worked with log() alot.
But from looking at it, you are given the interval of [1, 2].
All this problem is asking is is there any value that you can plug into x to make the function equal 4?
Well lets work this out. The smallest value you have in the interval [1, 2] is 1.
So plug that in and solve.
2¹ + log₂(1) = 2 + 0 = 2
The biggest value you have in the interval [1, 2] is 2.
So plug that in and solve.
2² + log₂(2) = 4 + some_fraction = 4.___
Usually the log of a number is some really small fraction. So we know that at k=2, the output is a bit greater than 4.
Therefore,
at 1 ≤ k ≤ 2
2 ≤ f(k) ≤ 4.___
in word form, when k is between 1 and 2, the output of the function will give you a number between 2 and 4.___ .
Since 4 lies between those two intervals, then some values of k between 1 and 2 will give you f(k)=4.
