22 Replies
@Apu
Note for OP
+solved @user to close the thread when your doubt is solved. Mention the user who helped you solve the doubt. This will be added to their stats.Bhai isme doubt kaha pr hai
konsa option hoga aur kyon?
Charo samjh ni aarhe? Ya kisi ek do m doubt hai
Pehle mai onto ka Pata chal gaya par onto ka Pata nahi
2 mai a ki har positive value pw hoga to bas us range ga galat hojayga par wo ans nahi Hai
3
Aur 4 nahi aa raha
anyone?
If you know basic differentiation, try to differentiate each function using power rule etc.
If your derivative changes signs, then that means your function curves from upward to downward or downward to upward
That means it cannot be injective
If you want to check if it is surjective, see where the derivative is not defined
eg: if the denominator is 0
Find the x coords of those places
Substitute in the main function
Also, substitutive +/- infinity in the main function
These give you the extreme values of the function so you can know the range
For 2nd option 'a' range does not match shouldn't it be the answer. Ans if 4
The first term in f(x) is x^3, not x^2, so there's an error
Mb it will be 3x^2 but still range is wrong
So if f(x) is one-one then the derivative should contain only one sign
So the derivative is 3x^2 + 2(a+2)x + 3a
ah, the derivative of 5 is 0, that's another thing
If this changes signs that means it has distinct roots, otherwise it has no distinct roots
So, let's find the interval of a such that that derivative has no distinct roots
Comrade Rock Astley
did you get the ideas here?
Oohhhh ok got it
I will try it
Sure
Ok I got the 3rd option
But how will we check 4th option?
Option 1 is not true right?
No option 4
How can we check 4th option?
the maximum value of acosx - bsin x is sqrt(a^2+b^2)
After that, use the derivative method
+solved @Comrade Rock Astley
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