AP EAMCET · Maths · Functions
If \(f: R \rightarrow A\) defined by \(f(x)=\frac{1}{x^2+2 x+2}\), \(\forall x \in R\) is surjective, then \(A=\)
- A \([1, \infty]\)
- B \((1, \infty)\)
- C \([0,1]\)
- D \((0,1]\)
Answer & Solution
Correct Answer
(D) \((0,1]\)
Step-by-step Solution
Detailed explanation
Since, the quadratic expression \[ \begin{aligned} & x^2+2 x+2=(x+1)^2+1 \in[1, \infty), \forall x \in R \\ \Rightarrow \quad & \frac{1}{(x+1)^2+1} \in(0,1] \end{aligned} \] For \(f(x)=\frac{1}{x^2+2 x+2}, \forall x \in R\) is surjective, then set \[ A=(0,1] \]
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