Question

Find the codomain of f(x) = (x+3) / (x-1)

Answer 1

Solution

- The question tells us to determine the codomain of the following rational function:

$f(x)=\frac{x+3}{x-1}$

- The codomain of the function is the possible values that f(x) can take.

; From the function, we can see that:

$\begin{gathered} f(x)=\frac{x+3}{x-1} \\ \text{when }x=1 \\ f(1)=\frac{1+3}{1-1}=\frac{4}{0} \\ \\ \text{Thus, f(1) leads to an undefined value. As such,} \\ x\ne1 \end{gathered}$

- Thus, we can conclude that the codomain is:

$undefined$