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Let f(x+y) + f(x-y) = 2f(x)f(y) for x, y...

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

A

One-one function

B

Onto function

C

Even function

D

Odd function

Text Solution

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The correct Answer is:
C
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AAKASH INSTITUTE-RELATIONS AND FUNCTIONS -Assignment (Section - B) Objective Type Questions (one option is correct)
  1. Which of the following function is an even function ?

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  2. A function f(x) given by f(x)={{:(x^(2)sin""(pix)/(2), |x| lt1),(x|...

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

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

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

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  7. Identify the incorrect statement

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

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

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  11. "If "f:R to R, g:R and h:R to R be three functions are given by f(x)=x...

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

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

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  14. Let f(x) be defined in (0, 1), then the domain of definition of f(e^...

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

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

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  17. If f(x) is a real valued function defined as f(x) = In(1 - sin x) then...

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

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  19. Select the correct option

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

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