Question

find the domain and range of x-1/x-3​

Answer 1

Given :  (x - 1)/(x - 3)

To Find : Domain and Range

Solution:

(x - 1)/(x - 3)

Domain is all real numbers except   when Denominator is zero

x - 3 = 0

=> x = 3

Hence Domain is  R - { 3 }

y = (x - 1)/(x - 3)

=> yx - 3y = x - 1

=> x(y - 1) = 3y - 1

=> x = (3y - 1)/(y - 1)

Hence x is not defined when y - 1= 0

Hence y ≠ 1

so Range is R - { 1 }

Domain is  R - { 3 }

Range is R - { 1 }

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