1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If ∣∣f(x) + 6 - x2∣∣ = |f(x)| + ∣∣4 - x2∣∣ + 2, then f(x) is necessarily non-negative in

A
[2,2]
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
(,2)(2,)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
[6,6]
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
none of these
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B [−2,2]|f(x)+6−x2|=|f(x)|+|4−x2|+2Above equation can also write it as,⇒ |f(x)+4−x2+2|=|f(x)|+|4−x2|+|2|We know, |a+b+c|=|a|+|b|+|c|, this is only possible if a,b,c are of same sign.Here, a=f(x),b=4−x2 and c=2 So, here f(x) and 2 are non-negative terms.4−x2 term also be non-negative∴ 4−x2≥0Multiplying by (−) sign we get,⇒ x2−4≤0⇒ (x+2)(x−2)≤0∴ x∈[−2,2]∴ f(x) is necessarily non-negative in x∈[−2,2]

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Properties of Inequalities
MATHEMATICS
Watch in App
Join BYJU'S Learning Program