Question

(x^ + 1) (x^-9)/(x^+2x+1) <= 0..find the value of x internal of x satisfying.​

Answer 1

Step-by-step explanation:

is

A

x∈(−∞,−

3

]∪[1,∞)

As, [x]−1+x

2

≥0;

⇒ x

2

−1≥−[x]

Thus, to find the points for which f(x)=x

2

−1 is greater than or equal to g(x)=−[x],

where the two functions f(x) and g(x) can be plotted as shown in the graph.

Thus, from the graph f(x)≥g(x) when x∈(−∞,A]∪[B,∞) where A is point of intersection of x

2

−1 and −[x]=+2

∴x

2

−1=+2 ie, x=−

3

=A and B=1

∴[x]−1+x

2

≥0 is satisfied, ∀x∈(−∞,−

3

]∪[1,∞)