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Which option (s) is/are ture ?...

Which option (s) is/are ture ?

A

`f :R to R, f (x) =e ^(|x|)-e ^(-x)` is many-one into function

B

`f : R to R, f (x)=2x+|sin x|` is one-one onto

C

`f:R to R, f (x)=(x^(2) +4x+30)/( x ^(2) -8x+18)` is many-one onto

D

`f :R to R, f (x) =(2x ^(2) -x+5)/( 7x^(2) +2x+10)` is many-one into

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The correct Answer is:
A, B, D
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VIKAS GUPTA (BLACK BOOK)-FUNCTION -ONE OR MORE THAN ONE ANSWE IS/ARE CORRECT
  1. Let f (x)= {{:(x ^(2),0lt x lt2),(2x-3, 2 le x lt3),(x+2, x ge3):} the...

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  2. Let f: [(2pi)/(3), (5pi)/(3)]to[0,4] be a function defined as f (x) =s...

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  3. Let f (x) be invertible function and let f ^(-1) (x) be is inverse. Le...

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  4. In function f(x)=cos^(-1)x+cos^(-1)(x/2+(sqrt(3-3x^2))/2) , then Range...

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  5. Let f:R rarr R defined by f(x)=cos^(-1)(-{-x}), where {x} denotes fra...

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  6. Which option (s) is/are ture ?

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  7. If f (x) =[ln (x)/(e) +[ln (e)/(x)], where [.] denotes greatest interg...

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  8. If f (x)= {{:(x ^(3), , x ∈ Q),(-x ^(3),,x ∉ Q):}, then :

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  9. Let f(x) be a real valued function such that f(0)=1/2 and f(x+y)=f(x)f...

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  10. f (x) is an even periodic function with period 10 In [0,5], f (x) = {{...

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  11. For the equation (e^-x)/(x+1) which of the following statement(s) is/a...

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  12. . For x in R^+, if x, [x], {x} are in harmonic progression then the va...

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  13. The equation ||x-1|+a | =4,a in R, has :

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  14. Let f (n)(x) = (sin x )^(1//pi) , x in R, then:

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  15. If the domain of f (x) =1/picos ^(-1)[log (3) ((x^(3))/(3))] where, x ...

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  16. The number of real values of x satisfying the equation;[(2x+1)/3]+[(4x...

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  17. Let f (x= sin ^(6) ((x )/(4)) + cos ^(6) ((x)/(4)). If f ^(n) (x) deno...

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  18. Which of the following is (are) incorrect ?

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  19. If [x] denotes the integral part of x for real x, and S= [(1)/(4)]+[(...

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  20. Let f(x) = log ({x}) [x] g (x) =log ({x})-{x} h (x) log ({x}) {x}...

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