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Let f(x) be periodic and k be a positive...

Let `f(x)` be periodic and `k` be a positive real number such that `f(x+k)+f(x)=0fora l lx in Rdot` Prove that `f(x)` is periodic with period `2kdot`

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ARIHANT MATHS-FUNCTIONS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let f(x) be periodic and k be a positive real number such that f(x+k)+...

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  2. If the function f(x)=x^(3)+e^(x//2)andg(x)=f^(-1)(x), then the value ...

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  3. Let F(x) be an indefinite integral of sin^(2)x Statement-1: The fun...

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  4. Find the range of values of t for which 2sint=(1-2x+5x^2)/(3x^2-2x-1)

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  5. Let F(k)(x)=1/k (sin^(k)x+cos^(k)x), where x in R and k ge 1, then fin...

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  6. Let f:R-R be defined as f(x) = x^4, then (a) f is one-one (b) f is man...

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  7. Let f(x)=x^2a n dg(x)=sinx for all x in R Then the set of all x satis...

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  8. Let f:(0,1)->R be defined by f(x)=(b-x)/(1-bx), where b is constant s...

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  9. Let f be a real-valued function defined on the inverval (-1,1) such th...

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  10. If X and Y are two non-empty sets where f: X->Y,is function is define...

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  11. If f(x)={x, when x is rational and 0, when x is irrational g(x)={0, w...

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  12. If f(x)=sinx+cosx, g(x)=x^(2)-1, then g(f(x)) is invertible in the do...

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  13. The domain of definition of the function f(x)=sqrt(sin^(-1)(2x)+pi/6) ...

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  14. The range of the function f(x)=(x^2+x+2)/(x^2+x+1),x in R , is (a) (...

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  15. If f:[0,infty) rarr [0,infty) " and " f(x)=x/(1+x), then f is

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  16. If f:R to R be defined by f(x) =2x+sinx for x in R, then check the na...

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  17. Let E={1,2,3,4} and F={1,2}dot If N is the number of onto functions fr...

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  18. Suppose f(x)=(x+1)^(2) " for " x ge -1. If g(x) is the function whos...

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  19. If F :[1,oo)->[2,oo) is given by f(x)=x+1/x ,t h e n \ f^(-1)(x) equal...

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  20. Let f(x)=(1+b^2)x^2+2b x+1 and let m(b) the minimum value of f(x)dot A...

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  21. Find the domain of the following functions. f(x)=(log(2)(x+3))/((x^(...

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