f-x-function-pair-and-0-decreases-in-the-range-f-x-f-3-solve-the-inequality-

Question Number 127322 by MathSh last updated on 28/Dec/20

f (x) f u n c t i o n p a i r a n d (- \infty; 0]

d e c r e a s e s i n t h e r a n g e

f (x) ⩾ f (- 3) s o l v e t h e i n e q u a l i t y

Answered by mindispower last updated on 28/Dec/20

] - \infty, - 3] \cup [3, + \infty [

Commented by MathSh last updated on 28/Dec/20

S o l u t i o n s i r p l i z

Commented by mindispower last updated on 28/Dec/20

s i n c e f d e c r e a s e

i n] - \infty, 0] \Rightarrow \forall x ⩽ - 3, f (x) ⩾ f (- 3)

\Rightarrow x \in] - \infty, - 3] i s s o l u t i o n

f (x) = f (- x) f e s t u n e f o n c t i o n p a i r e

\Rightarrow [3, \infty] e s t a u s s i s o l u t i o n

] - \infty, - 3] \cup [3, \infty [s o n t s o l u t i o n

m a i s p a s q u e c a r f p e u t e t r e c o n s t a n t e s u r

[- 3, 3] d a n s c e c a s S = R

e x e m p l e f (x) = {\begin{cases} x^{2}, x \in R - [- 3, 3] \\ 9 s i x \in [- 3, 3] \end{cases}

f (x) ⩾ f (- 3), l e s s o l u t i o n s o n t R t o u s e n t i e r