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Consider alpha gt 1 and f:[1/alpha,alpha...

Consider `alpha gt 1` and `f:[1/alpha,alpha] rarr [1/alpha,alpha]` be bijective function. Suppose that `f^(-1)(x)=1/f(x), " for all " in [1/alpha,alpha]`.
Which of the following statements can be concluded about (f(x))?

A

f(x) is discontinuous in `[1/alpha, alpha]`

B

f(x) is increasing in `[1/alpha, alpha]`

C

f(x) is decreasing in `[1/alpha, alpha]`

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
b
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ARIHANT MATHS-FUNCTIONS-Exercise (Passage Based Questions)
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  2. Let f(x)=1/2[f(xy)+f(x/y)] " for " x,y in R^(+) such that f(1)=0,f'(1)...

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  3. Let f(x)=1/2[f(xy)+f(x/y)] " for " x,y in R^(+) such that f(1)=0,f'(1)...

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  4. If f:R rarr R and f(x)=g(x)+h(x) where g(x) is a polynominal and h(x) ...

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  5. If f:R rarr R and f(x)=g(x)+h(x) where g(x) is a polynominal and h(x) ...

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  6. If f:R rarr R and f(x)=g(x)+h(x) where g(x) is a polynominal and h(x) ...

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  7. Let g(x)=a(0)+a(1)x+a(2)x^(2)+a(3)x^(3)andf(x)=sqrt(g(x)),f(x) have it...

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  8. Let g(x)=a(0)+a(1)x+a(2)x^(2)+a(3)x^(3)andf(x)=sqrt(g(x)),f(x) have it...

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  9. Let g(x)=a(0)+a(1)x+a(2)x^(2)+a(3)x^(3) " and " f(x)=sqrt(g(x)), f(x) ...

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  10. Let f :[2,oo)to {1,oo) defined by f (x)=2^(x ^(4)-4x ^(3))and g : [(pi...

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  11. Let f :[2,oo)to {1,oo) defined by f (x)=2^(x ^(4)-4x ^(3))and g : [(pi...

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  12. Let f:[2,infty) rarr [1, infty) defined by f(x)=2^(x^(4)-4x^(2)) and g...

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  13. Let P(x) be a polynomial of degree at most 5 which leaves remainders -...

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  14. Let P(x) be polynominal of degree atmost 5 which leaves remainders -1 ...

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  15. Let P(x) be polynominal of degree atmost 5 which leaves remainders -1 ...

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  16. Consider alpha gt 1 and f:[1/alpha,alpha] rarr [1/alpha,alpha] be bije...

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  17. Consider alpha gt 1 and f:[1/alpha,alpha] rarr [1/alpha,alpha] be bije...

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  18. Consider alpha gt 1 and f:[1/alpha,alpha] rarr [1/alpha,alpha] be bije...

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  19. Let f be real valued function from N to N satisfying. The relation f(m...

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  20. Let f be real valued function from N to N satisfying. The relation f(m...

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