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Verify that x sgnx=|x| |x|sgnx=x x(...

Verify that `x sgnx=|x|` `|x|sgnx=x` `x(sgnx)(sgnx)=x`

A

x sgn x = |x|

B

|x| sgn x = x

C

x (sgn x ) (sgn x) = x

D

| x| `(sgn x)^(3)` | x|

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The correct Answer is:
D
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DISHA PUBLICATION-RELATIONS AND FUNCTIONS -EXERCISE - 2
  1. Let f be a function on R given by f(x) = x^(2) and let E = {x in R: - ...

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  2. Let f(x)=x/(1+x^2) and g(x)=(e^-x)/(1+[x]), where [x] is the greatest ...

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  3. The relation R defined on the set A = {1, 2, 3, 4, 5} by R = {(a, b)...

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  4. Let f (x) = [x], where [x] denotes the greatest integer less than or e...

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  5. Define relations R(1) and R(2) on set A = [2,3,5,7,10] as xR(1)y is 2x...

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  6. A relation R is defined in the set Z of integers as follows (x, y ) in...

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  7. The domain of the function f(x)=sqrt(x^(2)-5x+6)+sqrt(2x+8-x^(2)) , ...

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  8. The real valued function f(x)=(a^x-1)/(x^n(a^x+1)) is even, then the v...

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  9. the value of the function f(x)=(x^2-3x+2)/(x^2+x-6) lies in the inter...

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  10. The domain of f (x) = log (|x - 2 | - 2 | - 1) is

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  11. If f:R to R satisfies f(x+y)=f(x)+f(y), for all x, y in R and f(1)=7,...

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  12. Find the domain of the following functions: f(x)=sqrt((2/(x^2-x+1)-1/(...

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  13. Which of the following functions is even,

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  14. If f(1) = 1 and f(n + 1) = 2 f(n) + 1, if n ge 1, then f(n) is.

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

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  16. Verify that x sgnx=|x| |x|sgnx=x x(sgnx)(sgnx)=x

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  17. The domain of the function f (x) = 3sqrt((x)/(1 - |x|))

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  18. The domain of the function f(x) = sqrt(x^(14) - x^(11) + x^(6) - x^(...

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  19. If f is any function, then (1)/(2) [ f (x) + f(-x) ] is always

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  20. The function f satisfies the functional equation 3f(x)+2f((x+59)/(x1))...

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