Answer to Question #141814 in Algebra for Haider

Question

Find the domain and range Of the function
f(x)=x-1/x-5 ,x is not equal to 5

Answer 1

$f(x)=\frac{x-1}{x-5};x\isin(-\infty,5)\cup(5,\infty)$

$f(x)=\frac{x-1}{x-5}=\frac{x-5+4}{x-5}=1+\frac{4}{x-5};\frac{4}{x-5}\not=0$

$f(x)\isin(-\infty,1)\cup(1,\infty)$

Answer domain-$(-\infty,5)\cup(5,\infty)$ ;range -$(-\infty,1)\cup(1,\infty)$