Questions
Which of the following functions is an injective (one-one) function in its respective domain?
detailed solution
Correct option is D
1 If fx=2x +sin3x ⇒ f'x =2 +3 cos3x =0 ⇒ cos 3x=-23 ,which is defined and f''x =- 9 sin3x = -35<0 so fx has maximum value exists in its domain , so it is not one-one2 fx = x.x is not one-one since f0.1=0.1 ×0 =0 and f0.2=0 3 fx=2x-14x+1 ⇒ fx is continuous function and f0=0 and fx →0 again when x→∞ since y =12x-14x1+14x →0 as x→∞ hence fx has a atleat one maximum exists , so it is not one-one4 fx =2x+14x-1 =2x+12x-12x+1 =12x-1 ⇒ f'x = -2x log22x-12<0 ⇒fx is decreasing function so it is one-oneTalk to our academic expert!
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