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

How do I get the range and also What does the the part to the right stating that x-example-1

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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\\e4

The second option is the correct answer

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