1can u please explain wat is injective and bijective function please
f(x)=ax3+bx2+cx+dsin x. Findthe condition that f(x) is always injective function.
2. Let f: X→Y be a function defined by f(x)= a sin(x+pi/4)+b cos x+c.If f(x) is bijective,find X.
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1
2621) b2-3a(c-d) <0 and b2-3a(c+d)<0
2) [2n*pi , 2(n+1)*pi) n→integer
262Hint :1) for f(x) to be injective, it should be either non-increasing or non-decreasing.
hence f(x) has only 1 real root,
therefore we can also say, f'(x) does not have 2 distinct real roots.
2) i dont know whats wrong with my answer
1@Aditya
Thank you veryyyy much.
Just a little more favour,Can you tell why f'(x) cant have two distinct roots.
Also answer to the second question contains a,b etc.
262abhinav, just try drawing a graph of a cubic function with three (distinct)real roots and then just one real root.
you will understand why.