Correct Answer: Option C

Explanation

Given that X  : R \(\to\) R is defined by x = \(\frac{y + 1}{5 - y}\) , y \(\in\) R, find the domain of x.

We need to identify the values of y for which the function is defined. The function is undefined when the denominator equals zero:

5 - y = 0 ⇒ y = 5 

This means that the function is not defined at y = 5

Thus, the domain of x includes all real numbers except y = 5.

In set notation, Domain of x = {y ∈ R y ≠ 5}

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