Solve this
Question:

$\mathrm{f}(\mathrm{x})=\frac{\mathrm{x}-5}{5-\mathrm{x}}$ then find dom (f) and range (f).

Solution:

Given, $f(x)=\frac{x-5}{5-x}$

(i) dom(f)

Here f(x) is a polynomial function whose domain is R except for points at which denominator becomes zero.

Hence x ≠ 5

The domain is $(-\infty, \infty)-\{5\}$

(ii) range(f)

Let $y=\frac{x-5}{5-x}$

For the specified domain

$y=-1$

Range is $\{-1\}$.