Which of the following is an injective function?
1).f(x)=2x+sin3x
2).f(x)=2^x-1/4^x+1
3).f(x)=2^x+1/4^x-1

Question

Which of the following is an injective function?
1).f(x)=2x+sin3x
2).f(x)=2^x-1/4^x+1
3).f(x)=2^x+1/4^x-1

samigupta8 · Answer

@faiqraees

samigupta8 · Answer

@jigglypuff314

samigupta8 · Answer

What i think is thT they all are injective..
Am i right??

samigupta8 · Answer

@phi

phi · Answer

I don't think I learned this.  (elec eng are different from math majors)

samigupta8 · Answer

Okay!! No issues..

samigupta8 · Answer

@directrix

samigupta8 · Answer

@hartnn

samigupta8 · Answer

@Ganeshie8

ganeshie8 · Answer

have you figured out the answer already ?

samigupta8 · Answer

Hartnn has told me about the graphs of these functions bt i want to solve the question by a proper way out ..
Like at first i weren't able to sketch out them...
So can you let me know if we have a definitive method to solve this problem??

hartnn · Answer

Ganesh, do you know of any specific method to find out whether the function is injective or not?

ganeshie8 · Answer

something like $f(a) = f(b) \implies a = b$ ?

samigupta8 · Answer

Yeah!! Can you solve like that for these functions ?? 
Not last one!

ganeshie8 · Answer

for the fist function you may simply use the derivative

ganeshie8 · Answer

the key thing to keep in mind here is that f'(x) cannot change signs if f(x) is injective

samigupta8 · Answer

Okay! We r getting the value of f'(x) ranging from (-1,5)

samigupta8 · Answer

Yep !! That's right!

ganeshie8 · Answer

that means f(x) is increasing at some region and decreasing at some other region : 

|dw:1458893171690:dw|