AP EAMCET · Maths · Functions
If \(R\) is the set of all real numbers and \(f: R-\{2\} \rightarrow R\) is defined by \(f(x)=\frac{2+x}{2-x}\) for \(x \in R-\{2\}\)
- A \(R-\{-2\}\)
- B \(R\)
- C \(R-\{1\}\)
- D \(R-\{-1\}\)
Answer & Solution
Correct Answer
(D) \(R-\{-1\}\)
Step-by-step Solution
Detailed explanation
Let \(y=f(x)=\frac{2+x}{2-x}\) \[ \begin{aligned} & \Rightarrow \quad 2 y-x y=2+x \\ & \Rightarrow \quad x(1+y)=2 y-2 \\ & \Rightarrow \quad x=\frac{2(y-1)}{1+y}, y \neq-1 \end{aligned} \] \(\therefore\) Domain of \(y\) is \(R-\{-1\}\). Hence, range of \(f(x)\) is \(R-\{-1\}\).
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