Asked by Anonymous
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,∞)
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,∞)
Answers
Answered by
Writeacher
https://www.jiskha.com/questions/1823673/solve-the-following-inequalities-if-it-is-known-that-function-g-is-decreasing-on-its
Answered by
Writeacher
I am so dumb I send another question to a question
Answered by
Anonymous
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.