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Let a real valued function f satisfy f(x...

Let a real valued function f satisfy `f(x + y) = f(x)f(y)AA x, y in R and f(0)!=0` Then `g(x)=f(x)/(1+[f(x)]^2)` is

A

An even function

B

An odd function

C

Neither even nor odd function

D

Periodic function

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The correct Answer is:
A
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AAKASH INSTITUTE ENGLISH-RELATIONS AND FUNCTIONS -Assignment (Section - B) Objective Type Questions (one option is correct)
  1. A function f(x) given by f(x)={{:(x^(2)sin""(pix)/(2), |x| lt1),(x|...

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  2. Let f(x+y) + f(x-y) = 2f(x)f(y) for x, y in R and f(0) != 0. Then f(x)...

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  3. Let a real valued function f satisfy f(x + y) = f(x)f(y)AA x, y in R a...

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  4. Let f: R rarr R be a function defined as f(x)=[(x+1)^2]^(1/3)+[(x-1)^2...

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  5. Let f(x) = |sinx| + |cosx|, g(x) = cos(cosx) + cos(sinx) ,h(x)={-x/2...

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  6. Identify the incorrect statement

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  7. Let f(x)=x^2 and g(x)=2^x . Then the solution set of the equation fo...

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  8. Let f(x) = tan x, x in (-pi/2,pi/2)and g(x) = sqrt(1-x^2) then g(f(x)...

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  9. Let g(x) be a polynomial function satisfying g(x).g(y) = g(x) + g(y) +...

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  10. If the functions f, g and h are defined from the set of real numbers R...

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  11. Range ofthe function f(x)=cos(Ksin x) is [-1,1], then the least positi...

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  12. Consider that the graph of y = f(x) is symmetrie about the lines x =...

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  13. The domain of f(x) is (0,1) .Then the domain of (f(e^x)+f(1n|x|) is (a...

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  14. If f(x) = 4^(x) - 2^(x + 1) + 5, then range of f(x) is

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  15. Let g be a real valued function defined on the interval (-1, 1) such t...

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  16. If f(x) is a real-valued function defined as f(x)=In (1-sinx), then t...

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  17. if f(x) is a real valued function defined as f(x)={min{|x|,1/x^2,1/x^3...

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  18. Select the correct option

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  19. Let f(x) = [x]^(2) + [x+1] - 3, where [.] denotes the greatest integer...

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  20. If 2^(f(x)) = (2+x)/(2-x), x in (-2, 2) and f(x) = lambda f((8x)/(4+ x...

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