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Let f: R to R be any function. Define g...

Let `f: R to R `be any function. Define `g : R to R` by `g(x) = | f(x)|, AA x`. Then, g is

A

onto if f is onto

B

one-one if f is one-one

C

continuous if f is continuous

D

differentiable if f is differentiable

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The correct Answer is:
C
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ML KHANNA-LIMITS, CONTINUITY AND DIFFERENTIABILITY -PROBLEM SET (2) (MULTIPLE CHOICE QUESTIONS)
  1. The function f(x) =[x] cos{(2x-1)//2} pi denotes the greatest integer...

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  2. The number of points where f(x) =[sin x + cos x] (where [.] denotes th...

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  3. Let f: R to R be any function. Define g : R to R by g(x) = | f(x)|, A...

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  4. If f(x) ={{:(x(e)^(-[1/|x|+1/x]), x ne 0),(0, x=0):}, then f(x) is:

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  5. The function f defined as - f(x) = (sin x^(2))//x for x ne 0 and f(0) ...

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  6. If f(x) = {{:(1, x lt 0),(1 + sinx, 0 le x lt pi//2):} Then at x=0, t...

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  7. For a real number y, let [y] denotes the greatest integer less than o...

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  8. If f(x) = x [sqrt(x) - sqrt(x+1)], then

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  9. The function f(x) = {{:(|x-3|, x ge 1),(x^(2)//4-3x//2 + 13//4, x lt 1...

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  10. The value of the derivative of |x-1| + |x-3| at x=2 is:

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  11. Let [ ] denote the greatest integer function and f(x) = [tan^(2)x] The...

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  12. If f(x) = {{:((|x+2|)/(tan^(-1)(x+2)), x ne -2),(2, x =-2):},

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  13. If f(x) = {{:( 3x ^(2) + 12 x - 1",", - 1 le x le 2), (37- x",", 2 lt...

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  14. The set of all points, where the function f(x) =x/(1+|x|) is differen...

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  15. The set of points where the function f(x) = x |x| is differentiable i...

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  16. Prove that the function If f(x)={:{((x)/(1+e^(1//x)) ", " x ne 0),(" ...

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  17. The set of allpoints of differentiability of the function f(x) ={{:(x^...

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  18. At the point x = 1, the function: f(x) = {{:(x^(3)-1, 1 lt x lt inft...

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  19. Let f(x) = "min" {1, x^(2), x^(3)}, then:

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  20. The function f(x) is defined as: f(x) =1/3 -x, x ,lt 1/3 =(1/3-x)^...

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