TS EAMCET · Maths · Functions
The range of the function defined by \(f(x)=\left\{\begin{array}{c}2 x-3, \text { if } x < -1 \ 1-x^2, \text { if }-1 \leq x \leq 1 \text { is } \ 3 x^2+2, \text { if } x>1\end{array}\right.\)
- A \(\mathbb{R}\)
- B \((-\infty,-5) \cup[0,1] \cup(5, \infty)\)
- C \((-\infty,-1) \cup(1, \infty)\)
- D \((-\infty,-3) \cup(0,1) \cup(3, \infty)\)
Answer & Solution
Correct Answer
(B) \((-\infty,-5) \cup[0,1] \cup(5, \infty)\)
Step-by-step Solution
Detailed explanation
\(f(x)=\left\{\begin{array}{cc}2 x-3 x < -1 \\ 1-x^2 -1 \leq x \leq 1 \\ 3 x^2+2 x>1\end{array}\right.\) Clearly the range is \((-\infty,-5) \cup[0,1] \cup(5, \infty)\)
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