Find the domain of the following hx squareroot t2 9 t2 9

Find the domain of the following h(x) = squareroot t^2 - 9 t^2 - 9 greaterthanorequalto 0 t^2 greaterthanorequalto - 9 g(x) = squareroot 2/x - 1 f(x) = x + 2/x^3 - 6x

Solution

Domain is the set of x values for which the function is defined.

A)

For h(x) to be defined we have

t^2 -9 >=0

=> t^2 - 3^2 >=0

=> (t+3)(t-3) >=0

hence t <= -3 and t> = 3

Therefore domian :-

B)

for g(x) to be defined

2/x-1> 0

=> x>1

Hence domain { x element R: x>1}

C)

f(x) = (x+2)/ (x^3 -6x)

denominator cannot be zero hence

x^3 - 6x = 0

x(x^2 -6) =0

x= 0 , x = sqrt6 , -sqrt 6

hence domian is all real values except the above three

hence domain