Answer to Question #248511 in Calculus for Jackson

Question

TOPIC 9: Domain Range of a Rational functions Find the domain and range of the following rational function

1.f(x)=2 x+1

2.f(x)=3x x+3

3.f(x)=3-x x-7

4.f(x)=2+x x

5.f(x)=(x+1) x^2-1

Answer 1

1) $f(x)=\frac{2}{x+1}. Domain: (-\infin,-1)\cup(-1,\infin).Range:(-\infin,0)\cup(0,\infin)$

2) $f(x)=\frac{3x}{x+3}. Domain: (-\infin,-3)\cup(-3,\infin).Range:(-\infin,3)\cup(3,\infin)$

3) $f(x)=\frac{2}{x+1}. Domain: (-\infin,-1)\cup(-1,\infin).Range:(-\infin,0)\cup(0,\infin)$

4) $f(x)=\frac{2+x}{x}. Domain: (-\infin,0)\cup(0,\infin).Range:(-\infin,1)\cup(1,\infin)$

5) $f(x)=\frac{x+1}{x^2-1}. Domain: (-\infin,1)\cup(1,\infin).Range:(-\infin,0)\cup(0,\infin)$