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f: R->R is defined by f(x)=(e^(x^2)-e^(-...

`f: R->R` is defined by `f(x)=(e^(x^2)-e^(-x^2))/(e^(x^2)+e^(-x^2))` is :

A

one-one but not onto

B

many-one but onto

C

one-one and onto

D

neither one-one nor onto

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The correct Answer is:
A
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OBJECTIVE RD SHARMA ENGLISH-FUNCTIONS-Chapter Test
  1. Let f : R rarr R, g : R rarr R be two functions given by f(x) = 2x - 3...

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  2. If g(x)=1+sqrtx and f(g(x))=3+2sqrtx+x then f(x) is equal to

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  3. If f(x)=(1-x)/(1+x), x ne 0, -1 and alpha=f(f(x))+f(f((1)/(x))), then

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  4. Let f:R to R be a function defined by f(x)=(x^(2)-8)/(x^(2)+2). Then f...

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  5. If f:(-oo,2]to (-oo,4] where f(x), then f ^(-1) (x) is given by :

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  6. Find the inverse of the function, (assuming onto). " " ...

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  7. f: R->R is defined by f(x)=(e^(x^2)-e^(-x^2))/(e^(x^2)+e^(-x^2)) is :

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  8. If f(x)=log((1+x)/(1-x))a n dt h e nf((2x)/(1+x^2)) is equal to {f(x)...

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  9. If f(x)=(2^x+2^(-x))/2 , then f(x+y)f(x-y) is equals to 1/2{f(2x)+f(2y...

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  10. The function f:R to R given by f(x)=x^(2)+x is

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  11. Let f:R to R and g:R to R be given by f(x)=3x^(2)+2 and g(x)=3x-1 for ...

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  12. The function of f:R to R, defined by f(x)=[x], where [x] denotes the g...

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  13. Let f(x)=x,g(x)=1/x and h(x)=f(x)g(x) . Then h(x)=1 for a.x in R b. x...

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  14. If the functions of f and g are defined by f(x)=3x-4 and g(x)=2+3x the...

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  15. If f(x)=(sin^(4)x+cos^(2)x)/(sin^(2)x+cos^(4)x)"for "x in R, then f(20...

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  16. The function f:R to R is defined by f(x)=cos^(2)x+sin^(4)x for x in R....

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  17. A = { x // x in R, x != 0, -4 <= x <= 4 and f: A -> R is defined by f...

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  18. If f: RvecR and g: RvecR are defined by f(x)=2x+3a n dg(x)=x^2+7, then...

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  19. Let f(x) be defined on [-2,2] and be given by f(x)={(-1",",-2 le x l...

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  20. The function f: R->R defined by f(x)=6^x+6^(|x|) is (a) one-one and on...

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