Question

If f is a continuous function defined for all real numbers x and the maximum value of f(x) is 5 and the minimum is -7, then which must be true?
I The maximum value of f(IxI) is 5
II The maximum value of If(x)I is 7
III The minimum value of f(IxI) is 0
those are absolute value marks

Answer 1

I

Answer 2

There's probably an actual rule to be applied here, but...

We have 3 important points here: \[f(a) = 5, f(b) = 0, f(c) = -7\] Because we don't have an actual graph, we cannot say anything about excluding the negative side of the graph which is what happens when we find the absolute value of x before putting it into f(x). We can, however, say that if the maximum before was 5 and the minimum was -7, after finding the absolute value there is now a point somewhere that has a value of 7. As this is higher than the previous maximum, II can be said to be true.
Therefore, The answer is II only.

Answer 3

number II is correct.

as I is maximum value of f(x>0) = 5, we dont know whether the maximum lies compared to x = 0
and II is maximum values of absolute value of f(x) = 7, as 7 is the largest value when we dont care about the sign this is true,
and III is the same case a I

Answer 4

Reread II: It says "The maximum value of If(x)I is 7," not "The maximum value of f(|x|) is 7

Answer 5

Ah, my apologies - you are correct.

Answer 6

I'm pretty sure II is right, I dont understand how I is

Answer 7

It is II, I misread the problem.

Answer 8

so I is not true at all?
because there is an option that includes both one and two

Answer 9

I isnt right, we dont know if the f(x) has a maximum of 5 when x > 0

Answer 10

1 is not necessarily true; if the maximum value of f(x) occurs when x < 0, then it won't be reachable in f(|x|) and thus the maximum value of f(|x|) will be less than 5.