Question

Which function has a domain where x does not =3 and a range where y does not =2? A. f(x)=(x-5)/(x+3) B. f(x)=2(x+5)/(x+3) C. 2(x+5)/(x-3) D. (x+5)/(x-3)

Answer 1

Answer: D. (x+5)/(x-3)

Step-by-step explanation:

Domain = Set of all input values of a function.

range = set of all output values of a function.

Given: Domain: $x\neq3$   ; range = $y\neq2$

We do not include a value for domain if it makes the expression indeterminant .

Since all the functions in options are fractions, here the denominator does not equal to 0.

But in option C and D, the denominator can be zero if x=3.

So , domain for then it $x\in {R-3}$

Also, for option C if $2=2\dfrac{(x+5)}{(x-3)}$

$\Rightarrow\ x-3=x+5\\\\\Rightarrow\ -3=5$.which is not true.

Wher as in option D, $2=\dfrac{x+5}{x-3}\Rightarrow\ 2x-6=x+5\Rightarrow\ x=11$

Hence, Domain: $x\neq3$   ; range = $y\neq2$ is for option D.