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Consider f:(0, oo)->(-pi/2,pi/2), defi...

Consider `f:(0, oo)->(-pi/2,pi/2)`, defined as `f(x) = tan^-1 (log_e x/((log_e x)^2+1))`. The about function can be classified as

A

Injective but nor surjective

B

Surjective but not bijective

C

Neither injective nor surjective

D

Both injective and surjective

Text Solution

Verified by Experts

The correct Answer is:
C
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ARIHANT MATHS-DEFINITE INTEGRAL-Exercise (Passage Based Questions)
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  2. Suppose lim(xrarr0)(int(0)^(x)(t^(2) dt)/((a+t^(r))^(1//p)))/(bx- sinx...

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  3. Suppose sum(x to 0)(int(0)^(x)(t^(2) dt)/((a+t^(r))^(1//p)))/(bx- sin...

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  4. Suppose f(x) and g(x) are two continuous functions defined for 0<=x<...

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  5. Suppose f(x) and g(x) are two continuous functions defined for 0<=x<...

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  6. Suppose f(x) and g(x) are two continuous functions defined for 0<=x<...

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  7. We are given the curvers y=int(- infty)^(x) f(t) dt through the point ...

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  8. We are given the curves y=int(-oo)^(x)f(t) dt through the point (0,(...

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  9. We are given the curvers y=int(- infty)^(x) f(t) dt through the point ...

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  10. f(x)=int(0)^(x) (4t^(4)-at^(3)) dt and g(x) is quadratic satifying g(...

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  11. f(x)=int(0)^(x) (4t^(4)-at^(3)) dt and g(x) is quadratic satifying g(...

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  12. f(x)=int(0)^(x) (4t^(4)-at^(3)) dt and g(x) is quadratic satifying g(...

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  13. If y = underset(u(x))overset(v(x))intf(t) dt, let us define (dy)/(dx) ...

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  14. Let y= int(u(x))^(y(x)) f (t) dt, let us define (dy)/(dx) as (dy)/(dx)...

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  15. If y = underset(u(x))overset(v(x))intf(t) dt, let us define (dy)/(dx) ...

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  16. Consider f:(0, oo)->(-pi/2,pi/2), defined as f(x) = tan^-1 (loge x/(...

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  17. The value of int(0)^(infty)[tan^(-1)x] dx is equal to (where ,[.] deno...

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