Question

How do I get the range and also What does the the part to the right stating that x≠1 mean as well?

Answer 1

Range of a function is all possible value of the dependent variable ( y-values) after which the domain (x-values ) have been substituted

For function f(x) = x + 3, the range would have been the set of all real numbers, but there is condition given which is x is not equal to 1 (x ≠ 1)

If x = 1, y will be

$\begin{gathered} y=x+3 \\ x=1 \\ y=1+3=4 \\ \text{Since the domain exclude 1, then the range will exclude the corresponding value of y, which is 4} \end{gathered}$

Hence, the range of the function f(x) will be

$y\ne4$

The second option is the correct answer