Sets, Relations & Functions
Functions and their properties
Grade 11
Question:
<p>If \(f(y) = \frac{x+1}{x-1}\), then \(f(y)\) is equal to</p>
<p>(a) \(x\)</p>
<p>(b) \(\frac{y+1}{y-2}\)</p>
<p>(c) \(\frac{x}{x+2}\)</p>
<p>(d) \(\frac{y-1}{y+2}\)</p>
Step-by-Step Solution
Key Concept: To find f(y), replace the variable x in the given expression with y, then simplify. The function definition remains the same regardless of what variable name is used as the input.
<p><strong>Step 1:</strong> Recognize that f is a function defined as f(x) = (x+1)/(x-1).</p><p><strong>Step 2:</strong> To find f(y), substitute y in place of x in the function definition.</p><p><strong>Step 3:</strong> f(y) = (y+1)/(y-1)</p><p>∴ Answer: A</p>
Correct Answer: A