find the domain and range of the function f(x)=x-3/2x+1 - Maths - Relations and Functions

Question

find the domain and range of the function f(x)=x-3/2x+1

Shridhar Kaushik · Accepted Answer

Given function is: $f (x) = \frac{x - 3}{2 x + 1}$ Domain of f: f (x) is defined if â€“ $2 x + 1 \neq 0 \Rightarrow 2 x \neq - 1 \Rightarrow x \neq - \frac{1}{2} Hence, Domain of f = R - {- \frac{1}{2}}$ Range of f: $Let y = \frac{x - 3}{2 x + 1} \Rightarrow 2 x y + y = x - 3 \Rightarrow x - 2 x y = y + 3 \Rightarrow x (1 - 2 y) = y + 3 \Rightarrow x = \frac{y + 3}{1 - 2 y}$ Now x assumes real values for all y except (1 â€“ 2y) = 0 $i e y = \frac{1}{2} Hence, Range of f = R - {\frac{1}{2}}$

find the domain and range of the function f(x)=x-3/2x+1.