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The inverse of the function f: Rvec{x in...

The inverse of the function `f: Rvec{x in R : x<1}` given by `f(x)=(e^x-e^(-x))/(e^x+e^(-x)),` is `1/2log(1+x)/(1-x)` (b) `1/2log(2+x)/(2-x)` `1/2log(1-x)/(1+x)` (d) None of these

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RD SHARMA ENGLISH-FUNCTION-All Questions
  1. If f(x)=3x-5, then f^(-1)(x) (a) is given by 1/((3x-5)) (b) is given...

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  2. If g(f(x))=|sinx|a n df(g(x))=(sinsqrt(x))^2 , then (a).f(x)=sin^2x ,g...

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  3. The inverse of the function f: Rvec{x in R : x<1} given by f(x)=(e^x-...

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  4. If the function f:(1,oo) vec (1,oo) is defined by f(x)=2^(x(x-1)),t h ...

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  5. Let A={x in R : xlt=1} and f: A->A be defined as f(x)=x(2-x). Then, f...

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  6. Let f(x)=1/(1-x) . Then, {f\ o\ (f\ o\ f)}(x)=(a) x for all x in R...

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  7. If the function f: R->R be such that f(x) = x-[x], where [x] denotes t...

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  8. If F :[1,oo)vec[2,oo) is given by f(x)=x+1/x ,t h e nf^(-1)(x) equals....

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  9. Let g(x)=1+x-[x]a n df(x)={-1, x<0;0, if x=0;1, ifx >0 . Then for all ...

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  10. Let f(x)=(alphax)/((x+1)),x!=-1. for what value of alpha is f(f(x))=x ...

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  11. The distinct linear functions which map [-1, 1] onto [0, 2] are f(x...

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  12. If f :[2,oo)rarr(-oo,4], where f(x)=x(4-x) then find f^-1(x)

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  13. If f: Rvec(-1,1) is defined by f(x)=-(x|x|)/(1+x^2),t h e nf^(-1)(x) e...

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  14. Let [x] denote the greatest integer less than or equal to x . If f(x...

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  15. If g(x)=x^2+x-2a n d1/2gof(x)=2x^2-5x+2, then which is not a possible ...

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  16. If f(x)=sin^2x and the composite function g(f(x))=|sinx| , then g(x)...

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  17. Let f: R->R be given by f(x)=x^2-3 . Then, f^(-1) is given by sqrt(x+3...

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  18. Let f(x)=x^3 be a function with domain {0, 1, 2, 3}. Then domain of...

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  19. Let f: R->R be given by f(x)=x^2-3 . Then, f^(-1) is given by (a)sqrt(...

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  20. Let f: R->R be given by f(x)=tanx . Then, f^(-1)(1) is pi/4 (b) {npi+p...

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