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A function f: R to R satisfies the equa...

A function `f: R to R` satisfies the equation `f(x+y) =f(x) f(y)` for all values of x and y and for any `x in R, f(x) ne 0`. Suppose the function is differentiable at x=0 and f' (0) = 2, then for all `x in R, f(x)=`

A

`e^(x)`

B

`e^(2x)`

C

`e^(-x)`

D

none

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The correct Answer is:
B
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ML KHANNA-LIMITS, CONTINUITY AND DIFFERENTIABILITY -PROBLEM SET (2) (MULTIPLE CHOICE QUESTIONS)
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  2. Consider, f(x) = {{:(x^(2)/(|x|), x ne 0),(0, x =0):}

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  3. The function f(x) = (x^(2)-1)|x^(2) -3x+2| + cos(|x|) is not differen...

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  4. Consider the following statements S and R: S: Both sin x and cos x a...

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  5. If f(x) =x^(2) + x^(2)/(1+x^(2)) + x^(2)/(1+x^(2))^(2) + …… + x^(2)/(1...

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  6. Let f(x) be a function satisfying f(x+y)=f(x)+f(y) and f(x)=x g(x)"For...

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  7. Let f(x + y)=f(x)+f (y) and f(x) = x^2 g(x) for all x, y in R, where g...

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  8. A differentiable function f (x) satisfies the condition f(x+y) =f(x) +...

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  9. Let f(x + y) = f(x) f (y) for all x and y. Suppose that f(3) = 3 and f...

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  10. Let f(x+y)=f(x) f(y) and f(x)=1+(sin 2x)g(x) where g(x) is continuous....

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  11. Suppose the function f satisfies the conditions : (i) f(x+y) =f(x) f...

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  12. A function f: R to R satisfies the equation f(x+y) =f(x) f(y) for al...

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  13. If f is twice differentiable function such that f''(x) =-f(x), and f...

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  14. Let F(x) =(f(x/2))^(2) +(g(x/2))^(2). F(5)=5 and f''(x) =-f(x), g(x) =...

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  15. If f'(x)=g(x) and g'(x)=-f(x) for all x and f(2) =4 =f'(2) then f^(2)(...

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  16. Let f(x+y) =f(x)f(y) for all x and y. Suppose f(5)=2 and f' (0) = 3, ...

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  17. Let f be a continuous function on [1,3] which takes rational values fo...

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  18. Let f(x) be differentiable AA x. If f(1)=-2 and f'(x) ge 2 AA x in x[1...

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  19. If f is a real valued differentiable function satisfying |f(x) -f(y)|...

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  20. Suppose f(x) is differentiable at x=1 and "lt"(h to 0)1/hf(1+h)=5 th...

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