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If f: R to R is defined by f(x) = 2x+|x|...

If `f: R to R` is defined by `f(x) = 2x+|x|`, then show that `f(3x) -f(-x) -4x=2f(x)`.

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AAKASH SERIES-FUNCTIONS -PRACTICE EXERCISE
  1. If f: R to R is defined by f(x) = 2x+|x|, then show that f(3x) -f(-x) ...

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  2. If f(x)=(3x-7)/(5x-3) then (fof)(x)=

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  3. If f:RR rarrRR and g:RR rarrRR are defined by f(x)=2x+3 and g(x)=x^(2)...

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  4. f: R to R is defined by f(x) =x^(2)-5x. Then the inverse image set of ...

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  5. If f: R to [0, infty) defined by f(x) = 10^(x) then f^(-1)(x)=

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  6. The range of 10^(-x) is:

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  7. The range of |x-2|+|x-5| is:

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  8. If A, B are two sets such that n(A) = 15, n(B) = 20, then the number o...

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  9. The number of surjections that can be defined from {1, 2, 3, 4, 5} ont...

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  10. The number of constant functions that can be defined from {1, 2, ……….,...

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  11. If f, g, h are functions from R to R such that f(x) = x^(2)+1, g(x) =s...

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  12. If f(x)=sin(logx), then f(xy)+f(x//y)-2f(x)cos (logy)=

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  13. If f(x)=(1)/(2)[3^(x)+3^(-x)], g(x)=(1)/(2)[3^(x)-3^(-x)] then f(x)g(y...

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  14. If f(x) =cos[pi^(2)]x + cos[-pi^(2)]x where [x] is symmetrical about t...

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  15. The graph of the function y = f(x) is symmetrical about the line x = 3...

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  16. Let f(x) = ax^(3) + bx +c. Then when f is odd,

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  17. a) The number of elements in the range of a constant function. (b) I...

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  18. The value of parameter alpha, for which the function f(x) =1+alphax, a...

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  19. Let f:[4, infty) to [1, infty) be a function defined by f(x) = 5^(x(x-...

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  20. If f: R to R and g: R to R are defined by f(x) =3x-4, g(x)=2+3x and 2(...

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  21. The domain of the definition of the function f(x) = sqrt(4^(x) + 8^(...

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