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Let f: R->R be a function defined by f(x...

Let `f: R->R` be a function defined by `f(x)=(e^(|x|)-e^(-x))/(e^x+e^(-x))` . Then, `f` is a bijection (b) `f` is an injection only (c) `f` is surjection on only (d) `f` is neither an injection nor a surjection

A

f (x) is many one, onto function

B

f (x) is many one, into function

C

f (x) is decreasing function `AA n in R `

D

`f (x)` is bijective function

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The correct Answer is:
B
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VIKAS GUPTA (BLACK BOOK) ENGLISH-FUNCTION -SUBJECTIVE TYPE PROBLEMS
  1. Let f: R->R be a function defined by f(x)=(e^(|x|)-e^(-x))/(e^x+e^(-x)...

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  2. Let f (x) be a polynomial of degree 6 with leading coefficient 2009, S...

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  3. Let f(x)=x^(3)-3x+1. Then number of different real solutions of f(f(x)...

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  4. If f(x+y+1)={sqrt(f(x))+sqrt(f(y))}^2 and f(0)=1AAx ,y in R ,d e t e ...

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  5. If the domain of f(x) = sqrt (12-3^(x)-3^(3-x))+ sin ^(-1) ((2x)/(3 ...

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  6. The number of elements in the range of the function : y =sin ^(-1) [...

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  7. The number of integers in the range of function f(x)= [sinx] + [cosx] ...

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  8. If P (x) is polynomial of degree 4 such than P (-1)=P (1) =5 and P (-2...

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  9. The number of integral vlaue (s) of k for which the curve y = sqrt ( ...

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  10. Let the solution set of the equation sqrt([x+[x/2]])+[sqrt({x})+[x/3]]...

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  11. For the real number x, let f (x)=(1)/( ""^(2011sqrt(1-x^(2011)))). Fi...

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  12. Find the number of elements contained in the range of the function f (...

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  13. Let f (x,y)= x^(2) - y^(2) and g (x,y)=2xy. such that (f ( x,y))^(2) -...

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  14. Let f (x) = (x+5)/(sqrt(x^(2) +1) ) , then the smallest integral va...

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  15. The number of roots of equation (((x-1)(x-3))/((x-2)(x-4))-e^(x)) (((x...

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  16. Let f (x) =x ^(2)-bx+c,b is an odd positive integer. Given that f (x)=...

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  17. Let f(x) be a continuous function such that f(0) = 1 and f(x)=f(x/7)=x...

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  18. If x=10 sum(r=3) ^(100) (1)/((r ^(2) -4)), then [x]= (where [.] deno...

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  19. Let f(x)= cx+d/ax+b ​ . Then fof(x) = x provided that.

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  20. Let A = {x|x ^(2) -4x+ 3 lt 0 , x in R} B={x|2^(1-x)+p le 0;x^2-2(p+7...

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  21. Let the maximum value of expression y= (x ^(4)-x ^(2))/(x ^(6) + 2x ^(...

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