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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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To prove that \([f(x)]^3 = f(x^3) + 3f(1/x)\) where \(f(x) = x + \frac{1}{x}\), we will follow these steps: ### Step 1: Calculate \(f(x)\) Given: \[ f(x) = x + \frac{1}{x} \] ...
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RD SHARMA-FUNCTIONS-Solved Examples And Exercises
  1. If f(x)=(x-1)/(x+1),x!=-1, . then show that f(f(x))=-1/x , prove that ...

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  2. Express the function f: XvecR given by f(x)=x^3+1 as set of ordered pa...

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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: AvecZ be function given by f(x)=...

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

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

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

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

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

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

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  17. Consider a rule f(x)=2x-3 associating elements of NN (set of natural n...

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  18. Let A={-2,\ -1,\ 0,\ 1,\ 2}a n d\ f: A->ZZ be given y f(x)=x^2-2x-3. F...

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  20. Let f : R - {2} rarr R be defined as f(x) = (x^2 - 4)/(x-2) and g: R...

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