Question

(x–3)(x+5)(x-7)/|x-4| (x+6)<= 0
The value of x satisfying,

Answer 1

Answer:

Correct option is

D

(−∞,−1)∪(−1,0)∪(1,∞)

log

∣x∣

(x

2

+x+1)≥0

log

x

(x

2

+x+1)≥0 (since, base of logarithm is to be positive)

Here, the base x can be either >1 or 0<x<1

Case I: When x>1

f(x)≥1

⇒x

2

+x+1≥1

⇒x(x+1)≥0

⇒x∈(−∞,−1)∪(0,∞) ....(1)

Case II: When 0<∣x∣<1

f(x)≤1

⇒x

2

+x+1≤1

⇒x(x+1)≤0

⇒x∈(−1,0) ....(2)

From (1) and (2), it follows that

x∈(−∞,−1)∪(−1,0)∪(1,∞)