Math Is Fun Forum

fusilli_jerry89

Member

Registered: 2006-06-23

Posts: 86

Inequalities

1) Find the set of points x satisfying:
a) x³ + x² ≤ 2x
b) |3-1/x| < 2

2) Show that any function with domain (-∞,∞) can be written as the sum of an odd function and an even function.

for 1(a) I got it down to: x(x+2)(x-1) ≤ 0. What to do next?
for 1(b): How do u get rid of the absolute value?

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Inequalities

1(a) There are four intervals: (i) x ≤ −2 (ii) −2 ≤ x ≤ 0 (iii) 0 ≤ x ≤ 1 (iv) x ≥ 1. In which of these intervals is x(x-1)(x+2) ≤ 0?

1 (b)

2

Last edited by JaneFairfax (2007-09-09 12:43:01)