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If f(x)=(x-1)/(x+1) , then show that f(1...

If `f(x)=(x-1)/(x+1)` , then show that `f(1/x)=-f(x)` (ii) `f(-1/x)=-1/(f(x))`

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RD SHARMA ENGLISH-FUNCTIONS-All Questions
  1. if for nonzero x, af(x) + bf(1/x) =1/x-5, where a!=b then f(2) =

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  2. If f(x) = (a-x^n)^(1/n), a > 0 and n in N, then prove that f(f(x)) = x...

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  3. If f(x)=(x-1)/(x+1) , then show that f(1/x)=-f(x) (ii) f(-1/x)=-1/(f(...

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  4. Find the domain and range of the function f(x) given by f(x)=(x-2)/(3-...

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  5. Find range of each of the following functions: 1. y=3sinx-2 2. y=2cosx...

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  6. Is g={(1,1),(2,3),(3,5),(4,7)} a function? If this is described by th...

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  7. Let f: R\rightarrowR be such that f(x)=2^x . Determine: Range of f (i...

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  8. Let f: R \rightarrowR be given by f(x)=x^2+3. Find (i) {x :f(x)=28} (i...

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  9. Find the domain and range of the function f(x)=1/(2-sin3x) .

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  10. If [x]^2-5[x]+6=0, where [.] denotes the greatest integer function, th...

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  11. If f is a real valued function given by f(x)=27 x^3+1/(x^3)a n dalpha,...

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  12. If 3f(x)+5f(1/x)=1/x-3 for all non-zero x , then f(x)= (a)1/(16)(...

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  13. The function f: R ⇒ R is defined by f(x)=cos^2x+sin^4x , r a n g e ...

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  14. If e^(f(x))=(10+x)/(10-x),x in (-10 ,10)a n df(x)=kf((200 x)/(100+x^2)...

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  15. The domain of definition of f(x)=sqrt((x+3)/((2-x)(x-5))) is (a)(-oo,-...

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  16. The range of the function f(x)=sqrt(5|x| - x^2 - 6) is equals to ...

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  17. If f: R \rightarrow R be given by f(x)=(4^x)/(4^x+2) for all x in Rdo...

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  18. If f(x)=sin[pi^2]x+sin[-pi^2]x, where [x] denotes the greatest integer...

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  19. If f is a real function defined by f(x)=(x-1)/(x+1), then prove that f...

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  20. If y=f(x)=(a x-b)/(b x-a) , show that x=f(y)dot

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