Question

If f is a continuous function defined for all real numbers x and if the maximum value of f(x) is 5 and the minimum value of f(x) is -7, then which of the following must be true?

I. the maximum value of f(lxl) is 5.
II. the maximum value of lf(x)l is 7.
III. the minimum value of f(lxl) is 0.

Answers:
A.) I only B.) II only C.) I and II only D.) II and III only E.) I, II, III

answer and please explain

Answer 1

option C. I and II only

Answer 2

the answer was b but idk y

Answer 3

ok.. lemme think..

Answer 4

oh yeah sorry, only II is right

Answer 5

can you explain the reason y please?

Answer 6

yes.. if the maximum value of f(x) is attained when x is negative, then I will not hold

Answer 7

II is true because |-7|=7

Answer 8

III may not be true.. minimum value of f(|x|) can be -7 too, if -7 is attained positive value of x

Answer 9

ok thanx

Answer 10

OH, I see it now! I was confused a bit at first...

f( |x| ) vs. | f(x) |
If you use x=|x|, it reflects the right side of the graph (for positive x) over the negative side.
If you take the absolute value of the function itself, it bounces off the x-axis when f(x) starts becoming negative, so you get the positive f(x) instead.

Answer 11

firstly nice pic !! the answer is B