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If f(x)=x+1/x , prove that [f(x)]^3=f(x^...

If `f(x)=x+1/x` , prove that `[f(x)]^3=f(x^3)+3f(1/x)dot` .

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RD SHARMA ENGLISH-FUNCTIONS-All Questions
  1. t f be defined by f(x)=x-4 and g be defined by g(x)={(x^2-16)/(x+4)...

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  2. Express the function f: X->R given by f(x)=x^3+1 as set of ordered pai...

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  3. If f(x)=x+1/x , prove that [f(x)]^3=f(x^3)+3f(1/x)dot .

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  4. Let f: RvecRa n dg: CvecC be two functions defined as f(x)=x^2a n dg(x...

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  5. Let A={12 ,13 ,14 ,15 ,16 ,17}a n df: A→Z be function given by f(x)= h...

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  6. Find the domain of each of the following functions given by f(x)=1/(sq...

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  7. Find the domain of definition of the following f(x) given by f(x)=log4...

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  8. Find the domain of definition of the function f(x) given by f(x)=1/(lo...

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  9. Find the range of each of the following functions: f(x)=|x-3| f(x)=...

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  10. Find the sum and product of identity function and the modulus function...

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  11. Let cb ea non-zero real number and f: RvecR be a function defined by f...

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  12. If f(x)=1/(1-x) , show thatf[f{f(x)}]=xdot

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  13. If f(x)=x^3-1/(x^3) , show that f(x)+f(1/x)=0.

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  14. Let fa n dg be two real functions defined by f(x)=1/(x+4)a n dg(x)=(x-...

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  15. Find the range of each of the following functions: f(x)=1/(sqrt(x-5)) ...

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  16. Find the domain of the real function f(x) defined by f(x)=sqrt((1-|x|)...

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  17. Let f be the exponential function and g be the logarithmic function, F...

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  18. If f is a real function satisfying f(x+1/x)=x^2+1/(x^2) for all x in ...

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  19. Let f\ be a relation on the set NN of natural numbers defined by f={(...

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  20. Let f be the subset of Z xxZ defined by f" "=" "{(a b ," "a" "+" "b)" ...

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