Which of the following statements is false?

Question

a) If x < 4, then |2x – 8| = 8 – 2x.

b) For all x, |x2 + x + 1| = x2 + x + 1.

c) For all x > 0, |x|/x2 = 1/x.

d) For all x < 0, |x|/x2 = 1/x.

e) At least one of the above statements is false.

NOTE: People sometimes squawk at (e). But if all of (a), (b), (c), and (d) are true, isn't (e) false? And similarly, if one of the first four is false, then (e) is true, isn't it?

Answer 1

i belive it is d. if you plug in a negative number for the first part |x|/x2, you will always get a positive number because the absolute value of all number is positive, as it the square of all numbers. On the other side, though, 1/x, if x is negative, the answer would be negative.

Answer 2

You must know the definition for |x|. That is |x| is x if x>=0 and |x| = -x if x<0. In other words: if the argument of y=|x| is positive or zero the function is y=x(repeat the argument), if the argument is negative then the function is y=-x(change the argument signal)
a) is true because for x<4 the function argument is negative, then
|2x-8|=-2x+8
c) is true because for x>0 |x|/x^2 = x/x^2=1/x
b) is true because the function argument is positive for x>0, then
|x^2+x+1| = x^2 + x + 1
d) is false because for x<0 |x|/x^2 = -x/x^2 = -1/x

Answer 3

I'm assuming by x2 you mean x^2 (x squared).

d) is false.

|x|/x^2 is always positive, since the numerator and denominator are always positive.

but when x < 0, 1/x is negative, so it can't be equal to
|x|/x^2.

that means

For all x < 0, |x|/x2 = 1/|x|

Because d) is false, e) is true.

Answer 4

D is false. |x|/x² always yields a positive value, whereas 1/x yields a negative value when x < 0.

Answer 5

I'd say that e is false. As far as I can tell, all of the others are true.

Answer 6

LizB is first correct answer.

Answer 7

e is false, because a,b,c,d are true

Answer 8

none of them