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

# If f(x+1x) = x3+1x3 (x â‰  0 ) then

A

f(x) is increasing function

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B

f(x) has a local maximum at x= -1

No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
C

f(x) is injective in its domain of definition

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D

The equation f (x) = 3 has a unique real root

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

## The correct options are A f(x) is increasing function C f(x) is injective in its domain of definition D The equation f (x) = 3 has a unique real root f(x+1x) = x3 + 1x3 = (x+1x)3 - 3x1x(x+1x) f(x)=x3−3x Since x+1x ≥ 2 for x > 0 and x+1x ≤ - 2,for x<0, the domain of f(x)is(−∞ , -2) ∪ [ 2 , ∞ ] f′(x) = 3 (x2 - 1) > 0 ∀ x ∈ D Thus f(x) is increasing in D , injective there and f(s)=3 has a unique real root. Since f is not defined at x = -1`, (b) does not hold

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Why Do We Need to Manage Our Resources?
MATHEMATICS
Watch in App
Join BYJU'S Learning Program