The minimum value of the function f(x)=∣∣2−|1−x|∣∣−1, where |x| denotes the absolute value of x, is
A
−1
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is A−1 Clearly, f(x) is defined for all real x. We know that the minimum value of modulus function is zero. So, 0≤∣∣2−|1−x|∣∣<∞,∀x∈R ⇒−1≤∣∣2−|1−x|∣∣−1<∞ ∴ Minimum value of f(x)=|2−|1−x||−1 is −1.