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(i) If f(x) = x + (1)/(x) prove that: ...

(i) If f(x) `= x + (1)/(x)` prove that:
`[f(x)]^(3) = f(x^(3)) + 3f ((1)/(x))`
(ii) If `f(x) = x^(3) - (1)/(x^(3))`, prove that `f(x) + f((1)/(x)) = 0`
(iii) If `f(x) = (1-x^(2))/(1+ x^(2))` , prove that `f (tan theta) = cos 2 theta`

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MODERN PUBLICATION-RELATIONS AND FUNCTIONS-Exercise 2(c )
  1. If f: A->B is an injection such that range of f={a} . Determine the...

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  2. (i) If f(x) = 3x^(4)- 5x^(2) + 7, " find " f(x-1) (ii) If f(x) = x^(...

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

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  4. (i) If y = f(x) = (3x-1)/(5x-3), prove that f(y) = x (ii) If y = f(x...

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  5. If f(x) = log(e) ((1-x)/(1+x)) , then f((2x)/(1 + x^(2))) is equal to...

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  6. (a) What are the real numbers x such that [x] =2? (b) What are the v...

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  7. What values does the function x rarr 2x^(2)-1 associate with the numbe...

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  8. Given f(x) = {(3x-8" for " ,x le5),(7 " for " ,x gt 5):} What is the...

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  9. What is the domain of the function (x)/(x^(2) - 3x + 2) ?

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  10. What is the range of the constant function 1 ?

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  11. For what values of x are the following functions not defined ? (i) (3x...

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  12. Find the periods of the following functions, if periodic : (i) | cos x...

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  13. Show that f: N->N defined by f(n)={(n+1)/2,\ \ if\ n\ i s\ od d n/2,\ ...

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  14. If f(x)=cos(logx), then f(x)f(y)-1/2[f(x/y)+f(xy)]=

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  15. (1) If f(x) = sqrt(x), prove that : (f(x + h) - f(x))/(h) = (1)/(sq...

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  16. Find domain(i) f(x) = (1)/(x - 5) (ii) f(x) = (3 - x)/(x - 3) (iii) f(...

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  17. (i) f(x) = sqrt(3 - 2x) (ii) f(x) = (1)/(sqrt(x + 2)) (iii) f(x) =...

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  18. Find the domain of f(x) = sqrt(log((5x - x^(2))/(6))

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  19. State, given justification for your answer, which of the following pai...

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  20. Are the following functions invertible in their respective domains ? I...

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