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Which of the functions defined below is ...

Which of the functions defined below is one one function ?

A

`f(x) = ((x^(3)+1)/(x^(4)+x^(2)+1)), (x in R)`

B

`g(x) = x + (1)/(x), (x in R^(+))`

C

`h(x) = x^(2) + 4x - 5(x in R)`

D

`f(x) = e^(-x), (x in R, x le 0)`

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The correct Answer is:
D
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AAKASH INSTITUTE-RELATIONS AND FUNCTIONS -Assignment (Section - B) Objective Type Questions (one option is correct)
  1. For real numbers x and y, we write x* y, if x - y +sqrt2 is an irratio...

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  2. If f(1)(x) = 2x + 3, f(2)(x) = 3x^(2) + 5, f(3)(x) = x + cos x are def...

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  3. Which of the functions defined below is one one function ?

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  4. Let f(x) = ax^(3) + bx^(2) + cx + d, a != 0, where a, b, c, d in R. If...

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  5. Let A = {1, 2, 3}, B = {a, b, c}, C {a(1), b(1), c(1), d(1), e(1)} an...

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  6. Select the correct option

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  7. Let f : [2, 4) rarr [1, 3) be a function defined by f(x) = x - [(x)/(2...

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  8. Identify the correct option

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  9. Which of the following function is an even function ?

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

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

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

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

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  15. Identify the incorrect statement

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

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

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

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