Most Important Selected Qs for JEE AdvancedMathematicsFunctions

f: R R is defined as f(x)= [ array ll x^2+2 m x-1 & for x 0 m x-1 & for x 0 array . . If f(x) is one-one then m must lies in the interval

Options

A(- , 0)
B(- , 0]
C(0, )
D[0, )

Correct answer

A. (- , 0)

Step-by-step solution

for f^2 to be one-one f^ (x) 0 and f^ (x) 0 for all x clearly f is continuous at x=0 and f(0)=-1x 0, f^ (x)=2(x+m) for x 0f^ (x) can not be 0 for x 0 if m 0 f ^ ( x ) 0 for m 0 but m 0 as for x 0, f is constant and m 0, f ^ ( x ) 0, x 0

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