TS EAMCET · Maths · Application of Derivatives
If \(\quad f:[2, \infty) \rightarrow B \quad\) defined by \(f(x)=x^2-4 x+5\) is a bijection, then \(B\) is equal to
- A \([0, \infty)\)
- B \([1, \infty)\)
- C \([4, \infty)\)
- D \([5, \infty)\)
Answer & Solution
Correct Answer
(B) \([1, \infty)\)
Step-by-step Solution
Detailed explanation
Given, \(f(x)=x^2-4 x+5\) On differentiating w.r.t. \(x\), we get \(f^{\prime}(x)=2 x-4\) Put \(f^{\prime}(x)=0 \Rightarrow x=2\) For \(x>2, f^{\prime}(x)>0\), increasing \(\therefore\) Minimum value is \(f(2)=4-8+5=1\) \(\therefore \quad B \in[1, \infty)\)
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