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Assertion (A) : If f : R to R defined by...

Assertion (A) : If `f : R to R` defined by `f(x) =sin^(-1)(x/2) + log_(10)^(x)`, then the domain of the function is (0,2].
Reason (R) : If `D_(1)` and `D_2` are domains of `f_(1)` and `f_2` , then the domain of `f_(1) + f_(2)` is `D_(1) cap D_(2)`

A

Both A and R are true and R is the correct explanation of A

B

Both A and R are true but R is not correct explanation of A

C

A is true but R is false

D

A is false but R is true

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The correct Answer is:
A
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AAKASH SERIES-FUNCTIONS -PRACTICE EXERCISE
  1. If f:[0, oo) to [0,oo) is defined by f (x) = (x)/(1+ x) , then f is

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  2. Statement-1: f : R -{0} to R-{0} defined by f(x) =1/x is bijective ...

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  3. If A = {1, 2, 3,4} and B = {x, y, z, w} , then a) Number of mappings...

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  4. Observe the following Lists: Then the match for List -1 from Lis...

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  5. The domain of Cos^(-1).(x-3)/(2)-log(10(4-x) is

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  6. Assertion (A) : If f : R to R defined by f(x) =sin^(-1)(x/2) + log(10)...

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  7. Domain of tan^(-1)3x is:

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  8. The domain of f(x) = (sin^(-1)x)/([x]) is:

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  9. The domain of (tanh^(-1)(3x-2))/sqrt(16-9x^(2)) is

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  10. I : Every strictlyy monotonic function is one one. II : The function...

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  11. If f: C to R such that f(z) =Re(z), then f is:

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  12. If f: C to R such that f(z) =Re(z), then f is:

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  13. A real valued function f(x) satisfies the functional equation f(x-y) =...

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  14. The function f:NrarrZ defined by f(n)=(n-1)/(2) when n is odd and f(n)...

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  15. Let f(x) = sinx + cosx, g(x) =x^(2)-1. Then g(f(x)) is invertible for ...

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  16. The domain of the function: f(x) = (sin^(-1)(x-3))/sqrt(9-x^(2)) is:

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  17. Let f:(-1,1) to B, be a function defined by f(x) = tan^(-1)((2x)/(1-x^...

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  18. For real x, let f(x) =x^(3) + 5x+1, then

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  19. Let the function f: R to R be defined by f(x) = 2x + sinx for x in R, ...

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  20. If f(x) +2f(1/x) =3x, x ne 0 and S={x in R//f (x) =f(-x)}, then S is:

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