D Given, \(f(x)=\sqrt{\cos x}\) Then, \(\quad \cos x \geq 0\) \(x\) should be lies in I and IV quadrant including ends of the quadrant \(\Rightarrow \mathrm{x} \in \mathrm{Z},\left[2 \mathrm{n} \pi+0,2 \mathrm{n} \pi+\frac{\pi}{2}\right] \cup\left[2 \mathrm{n} \pi+\frac{3 \pi}{2}, 2 \mathrm{n} \pi+2 \pi\right]\) where, \(\mathrm{n} \in \mathrm{Z}\), for \(\mathrm{n}=0\) \(\therefore \quad \mathrm{x} \in\left[0, \frac{\pi}{2}\right] \cup\left[\frac{3 \pi}{2}, 2 \pi\right]\)
Karnataka CET-2014
Sets, Relation and Function
117377
Let \(f:[2, \infty) \rightarrow R\) be the function defined by \(f(x)=x^2-4 x+5\), then the range of \(f\) is
1 \([1, \infty)\)
2 \((1, \infty)\)
3 \([5, \infty)\)
4 \((-\infty, \infty)\)
Explanation:
A Given, \(f:[2, \infty) \rightarrow R\) \(f(x)=x^2-4 x+5\) \(f(2)=2^2-4 \times 2+5\) \(f(2)=4-8+5\) \(f(2)=1\) \(f(\infty)=(\infty)^2-4(\infty)+5\) \(f(\infty)=\infty\)Hence, range \(=[1, \infty)\)
Karnataka CET-2020
Sets, Relation and Function
117378
The domain of the function \(f: R \rightarrow R\) defined by \(f(x)=\sqrt{x^2-7 x+12}\) is
D Given, \(f(x)=\sqrt{\cos x}\) Then, \(\quad \cos x \geq 0\) \(x\) should be lies in I and IV quadrant including ends of the quadrant \(\Rightarrow \mathrm{x} \in \mathrm{Z},\left[2 \mathrm{n} \pi+0,2 \mathrm{n} \pi+\frac{\pi}{2}\right] \cup\left[2 \mathrm{n} \pi+\frac{3 \pi}{2}, 2 \mathrm{n} \pi+2 \pi\right]\) where, \(\mathrm{n} \in \mathrm{Z}\), for \(\mathrm{n}=0\) \(\therefore \quad \mathrm{x} \in\left[0, \frac{\pi}{2}\right] \cup\left[\frac{3 \pi}{2}, 2 \pi\right]\)
Karnataka CET-2014
Sets, Relation and Function
117377
Let \(f:[2, \infty) \rightarrow R\) be the function defined by \(f(x)=x^2-4 x+5\), then the range of \(f\) is
1 \([1, \infty)\)
2 \((1, \infty)\)
3 \([5, \infty)\)
4 \((-\infty, \infty)\)
Explanation:
A Given, \(f:[2, \infty) \rightarrow R\) \(f(x)=x^2-4 x+5\) \(f(2)=2^2-4 \times 2+5\) \(f(2)=4-8+5\) \(f(2)=1\) \(f(\infty)=(\infty)^2-4(\infty)+5\) \(f(\infty)=\infty\)Hence, range \(=[1, \infty)\)
Karnataka CET-2020
Sets, Relation and Function
117378
The domain of the function \(f: R \rightarrow R\) defined by \(f(x)=\sqrt{x^2-7 x+12}\) is
D Given, \(f(x)=\sqrt{\cos x}\) Then, \(\quad \cos x \geq 0\) \(x\) should be lies in I and IV quadrant including ends of the quadrant \(\Rightarrow \mathrm{x} \in \mathrm{Z},\left[2 \mathrm{n} \pi+0,2 \mathrm{n} \pi+\frac{\pi}{2}\right] \cup\left[2 \mathrm{n} \pi+\frac{3 \pi}{2}, 2 \mathrm{n} \pi+2 \pi\right]\) where, \(\mathrm{n} \in \mathrm{Z}\), for \(\mathrm{n}=0\) \(\therefore \quad \mathrm{x} \in\left[0, \frac{\pi}{2}\right] \cup\left[\frac{3 \pi}{2}, 2 \pi\right]\)
Karnataka CET-2014
Sets, Relation and Function
117377
Let \(f:[2, \infty) \rightarrow R\) be the function defined by \(f(x)=x^2-4 x+5\), then the range of \(f\) is
1 \([1, \infty)\)
2 \((1, \infty)\)
3 \([5, \infty)\)
4 \((-\infty, \infty)\)
Explanation:
A Given, \(f:[2, \infty) \rightarrow R\) \(f(x)=x^2-4 x+5\) \(f(2)=2^2-4 \times 2+5\) \(f(2)=4-8+5\) \(f(2)=1\) \(f(\infty)=(\infty)^2-4(\infty)+5\) \(f(\infty)=\infty\)Hence, range \(=[1, \infty)\)
Karnataka CET-2020
Sets, Relation and Function
117378
The domain of the function \(f: R \rightarrow R\) defined by \(f(x)=\sqrt{x^2-7 x+12}\) is
D Given, \(f(x)=\sqrt{\cos x}\) Then, \(\quad \cos x \geq 0\) \(x\) should be lies in I and IV quadrant including ends of the quadrant \(\Rightarrow \mathrm{x} \in \mathrm{Z},\left[2 \mathrm{n} \pi+0,2 \mathrm{n} \pi+\frac{\pi}{2}\right] \cup\left[2 \mathrm{n} \pi+\frac{3 \pi}{2}, 2 \mathrm{n} \pi+2 \pi\right]\) where, \(\mathrm{n} \in \mathrm{Z}\), for \(\mathrm{n}=0\) \(\therefore \quad \mathrm{x} \in\left[0, \frac{\pi}{2}\right] \cup\left[\frac{3 \pi}{2}, 2 \pi\right]\)
Karnataka CET-2014
Sets, Relation and Function
117377
Let \(f:[2, \infty) \rightarrow R\) be the function defined by \(f(x)=x^2-4 x+5\), then the range of \(f\) is
1 \([1, \infty)\)
2 \((1, \infty)\)
3 \([5, \infty)\)
4 \((-\infty, \infty)\)
Explanation:
A Given, \(f:[2, \infty) \rightarrow R\) \(f(x)=x^2-4 x+5\) \(f(2)=2^2-4 \times 2+5\) \(f(2)=4-8+5\) \(f(2)=1\) \(f(\infty)=(\infty)^2-4(\infty)+5\) \(f(\infty)=\infty\)Hence, range \(=[1, \infty)\)
Karnataka CET-2020
Sets, Relation and Function
117378
The domain of the function \(f: R \rightarrow R\) defined by \(f(x)=\sqrt{x^2-7 x+12}\) is