Question

Find the domains

Answer 1

a)

1)

The function f(x)  =  √(2x - 1)

Negative of root values doesnot exist 

Hence 

2x - 1  ≥  0

2x  ≥  1

x  ≥  1/2

Therefore, Domain is  [1/2, infinity )

2)

The function g(x)  =  5/(x^2)

If x = 0 the function g(x) is undefined

Hence,

Domain is ( -infinity , 0 ) U ( 0, infinity )

b)

g o f (x)  =  g( f(x) )

              =  g( √(2x - 1)

              =  5 / [ √(2x - 1) ]^2

              =  5 / (2x - 1)

Answer :

a)

1)  Domain : [1/2, infinity )

2)  Domain : ( -infinity , 0 ) U ( 0, infinity )

b)

g o f (x)  =  5 / (2x - 1).