Find the domain and range of f(x)=1/x-3 Iam quite confident about the domain so please tell me the range!!!!!! - Maths - Relations and Functions

Question

Find the domain and range of f(x)=1/x-3
Iam quite confident about the domain so please tell me the
range!!!!!!

Ajanta Trivedi · Accepted Answer

the given function is $f (x) = \frac{1}{x - 3}$

since the denominator can not be zero for real values of f(x).

therefore $x - 3 \neq 0 \Rightarrow x \neq 3$

thus domain of the function is $x \in (- \infty, \infty) - {3} i . e . R - {3}$

now for range let $y = \frac{1}{x - 3}$

$x - 3 = \frac{1}{y} x = 3 + \frac{1}{y} x = \frac{3 y + 1}{y}$

thus for real values of x , $y \neq 0$

thus range = $(- \infty, 0) \cup (0, \infty) i . e . R - {0}$

hope this helps you.

cheers!!

Find the domain and range of f(x)=1/x-3. Iam quite confident about the domain so please tell me the range!!!!!!.