Can anyone explain how this math (function) problem is even possible

This is what the whole function is:

f(x) =
{2x -1; if -2 ≤ x ≤ 5
{x^3 - 5; if 5 < x ≤ 6

This is the function you're supposed to solve: f(5)

So if we incorporate f(5) into both equations, we'd get these two as the answers:

f(x) = 2x - 1
f(5) = 2(5) - 1
f(5) = 9

f(x) = x^3 - 5
f(5) = (5)^3 - 5
f(5) = 120

Now the problem I'm having with this is that my textbook states that the answer to the function problem should only be "f(5) = 9", and not "f(5) = 120". But it doesn't even state a reason why 9 would be the actual answer. The confusing part of this is really the "if" part. Now if I'm reading the "greater than/less than" scales to each equation right, it specifically states that in order for "9" to be the correct answer to function problem, the answer (9) must be a number "LESS than or equal to -2, and LESS than or equal to 5". So why would "9" be the answer to the problem if it is MORE than both "-2" and "5"? I would've thought the answer would've been "none" for both of the equations since both "9" and "120" are numbers "more" than what exceeds the scale. Please help me here, this is so confusing.

Lindsay,

This type of function is called a piecewise function. It consists of two equations with given intervals.

The first piece has an interval of -2 ≤ x ≤ 5. In English terms, this says "use piece one when the x-value is less than OR EQUAL TO 5, and greater than OR EQUAL TO -2."

The second piece has an interval of 5 < x ≤ 6. In English terms, this says "use piece two when x is greater than BUT NOT EQUAL TO 5, and less than or equal to 6."

The < or > sign indicates that the number being compared with x is not actually part of the piece, but that the function approaches at that point.