Question

Find the domain of the function

a) f(x) = 1 / x-3

b) f(x) = 1 / 3x-6

c) f(x) = x+2 / x^2-1

d) f(x) = x^4 / x^2+x-6

Answer 1

Given

a) f( x ) = 1 / ( x - 3 )

=> x belongs to R , 3 is not included

domain ----> ( - ∞ , 3 ) U ( 3 , ∞ )

b) f( x ) = 1 / ( 3*x - 6 )

f( x ) = 1 / [ 3*( x - 2 ) ]

=> x belongs to R , 2 is not included

domain ----> ( - ∞ , 2 ) U ( 2 , ∞ )

c) f( x ) = ( x + 2 ) / ( x^2 - 1 )

=> f( x ) = ( x + 2 ) / [ ( x - 1 )*( x + 1 ) ]

x is undefined at x = - 1 and x = 1

domain ----> ( - ∞ , - 1 ) U ( - 1 , 1 ) U ( 1 , ∞ )

d) f( x ) = x^4 / ( x^2 + x - 6 )

=> f( x ) = x^4 / ( x^2 + 3*x - 2*x - 6 )

=> f( x ) = x^4 / ( x*( x + 3 ) - 2*( x + 3 ) )

=> f( x ) = x^4 / ( x + 3 )*( x - 2 )

x is undefined at x = - 3 and x = 2

domain ----> ( - ∞ , - 3 ) U ( - 3 , 2 ) U ( 2 , ∞ )