Solve the following inequalities, if it is known that function f is increasing on its domain.
1. f(x^3−4x)≥f(3x^2+6x), Df=ℝ
2. f(x^4−x) 3. f(4x−3)≥f(2−x^2), Df=(−8,4)
4. f(x^2−5x−7)≤f(5−6x), Df=[−1,∞)
3 answers
https://www.jiskha.com/questions/1823673/solve-the-following-inequalities-if-it-is-known-that-function-g-is-decreasing-on-its
I am so dumb I send another question to a question
For the first one, because the function is increasing and the domain is all real numbers, you can just get rid of the function sign. this changes it to:
x^3-4x>=3x^2+6x
x^3-3x^2-10x>=0
factor:
x(x-5)(x+2)>=0
use the snake method to solve and you will get:
x belongs from [-2,0]U[5,infinity)
for the others do the same thing, except if you have f(a)>f(b) and the domain is Df>c then you have to make sure that a>c and b>c, other than that though you will solve it the same way as the first.
x^3-4x>=3x^2+6x
x^3-3x^2-10x>=0
factor:
x(x-5)(x+2)>=0
use the snake method to solve and you will get:
x belongs from [-2,0]U[5,infinity)
for the others do the same thing, except if you have f(a)>f(b) and the domain is Df>c then you have to make sure that a>c and b>c, other than that though you will solve it the same way as the first.