Write the domain and the range of the function, f(x) = \(\frac{ax+b}{

1.	Write the domain and the range of the function, f(x) = \(\frac{ax+b}{bx-a}\).
Answer» (i) domain f(x) = \(\frac{ax+b}{bx-a}\) As f(x) is a polynomial function whose domain is R except for the points where the denominator becomes 0. Hence x ≠ a/b Domain is R a/{-b} (ii) Range Let y = \(\frac{ax+b}{bx-a}\) Y(bx-a) = ax +b byx -ay = ax + b byx -ax= ay +b x(by -a) = ay + b x = \(\frac{ay+b}{by-a}\) x is not defined when denominator is zero. by – a ≠ 0 y ≠ a/b Range is R-{a/b}.

Write the domain and the range of the function, f(x) = \(\frac{ax+b}{bx-a}\).

Answer»

(i) domain

f(x) = \(\frac{ax+b}{bx-a}\)

As f(x) is a polynomial function whose domain is R except for the points where the denominator becomes 0.

Hence x ≠ a/b

Domain is R a/{-b}

(ii) Range

Let y = \(\frac{ax+b}{bx-a}\)

Y(bx-a) = ax +b

byx -ay = ax + b

byx -ax= ay +b

x(by -a) = ay + b

x = \(\frac{ay+b}{by-a}\)

x is not defined when denominator is zero.

by – a ≠ 0

y ≠ a/b

Range is R-{a/b}.