The domain of f(x)=log_1/4[(5x-x²)]/2 + ¹⁰C_x is

1.(0,1]U[4,5)

2.(0,5)

3.{1,4}

4.None of these

2.(0,5)

AS 1/4 <1 FOR log FUNCTION TO BE DEFINED

      0<5x-(x^2)<1

    solving independently we get

     0<x<5 and x>4.79 ,x<0.208 

     so  solution set is (0,0.208)U(4.79,5) 

      BUT FOR 10 C X TO BE DEFINED 0<X<10 ,X=0,10

    SO THERE IS NO SOLUTION SET FOR THE DOMAIN OF THIS FUNCTION

Hi Menka,

For domain questions, you should find the interval of x (ie the independent variable) where the function f(x) is well defined.

Now for C(10,x) to be defined, x has to be a whole number. So straight away option 1 and option 2 are incorrect options.

Now for Log(X), the domain is X > 0.

So here, 5x-x^2 > 0,

ie x^2 - 5x < 0

or x*(x-5) < 0

or 0 < x < 5.

Now our f(x) is the addition of two functions. So for f(x) to be well defined, the interval of x should be such that, both functions together are well defined. So we take the intersection of the intervals of (0,5) and {set of whole numbers}

That will give the set as {1,2,3,4}

So these are the only four values that x can take. Hence option 4.None of these.

Hope that helps!!.

Regards,

Ashwin (IIT Madras)