IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

Sree

Find Domain?

f(x)=^{[2 ]}

((-log_x-3(x-1))(^{[2 ]}

-x²+2x+8)).

puneet

hii

well, see let us do it like this .. for each term we find out the condition on x and then try to get intersection of all ..

x - 3 > 0 .. (1)

x - 1 > 0 .. (2)

also, - log_x-3(x-1) > 0 ( since it is in the sq rt sign )

Now, from (1) and (2) we know that x > 3

we want log_x-3(x-1) < 0 , so now x - 1 > 2 , so x - 3 < 1 is the only way left to make it less than 0

thus we get x < 4 ... (3)

combining (1) and (3) we get,

3 < x < 4 ... (4)

Now the term -x²+2x+8 > 0

or, 9 - (x - 1)² > 0

which means 3 > x - 1 > -3

or, 4 > x > - 2 .. (5)

From (4) and (5) we get

3 < x < 4 .. Ans

cheers

puneet

hii