1
JEE Main 2024 (Online) 27th January Evening Shift
+4
-1

Let $$f: \mathbf{R}-\left\{\frac{-1}{2}\right\} \rightarrow \mathbf{R}$$ and $$g: \mathbf{R}-\left\{\frac{-5}{2}\right\} \rightarrow \mathbf{R}$$ be defined as $$f(x)=\frac{2 x+3}{2 x+1}$$ and $$g(x)=\frac{|x|+1}{2 x+5}$$. Then, the domain of the function fog is :

A
$$\mathbf{R}-\left\{-\frac{7}{4}\right\}$$
B
$$\mathbf{R}$$
C
$$\mathbf{R}-\left\{-\frac{5}{2},-\frac{7}{4}\right\}$$
D
$$\mathbf{R}-\left\{-\frac{5}{2}\right\}$$
2
JEE Main 2024 (Online) 27th January Morning Shift
+4
-1
The function $f: \mathbf{N}-\{1\} \rightarrow \mathbf{N}$; defined by $f(\mathrm{n})=$ the highest prime factor of $\mathrm{n}$, is :
A
one-one only
B
neither one-one nor onto
C
onto only
D
both one-one and onto
3
JEE Main 2023 (Online) 13th April Evening Shift
+4
-1

The range of $$f(x)=4 \sin ^{-1}\left(\frac{x^{2}}{x^{2}+1}\right)$$ is

A
$$[0,2 \pi]$$
B
$$[0,2 \pi)$$
C
$$[0, \pi)$$
D
$$[0, \pi]$$
4
JEE Main 2023 (Online) 13th April Morning Shift
+4
-1

For $$x \in \mathbb{R}$$, two real valued functions $$f(x)$$ and $$g(x)$$ are such that, $$g(x)=\sqrt{x}+1$$ and $$f \circ g(x)=x+3-\sqrt{x}$$. Then $$f(0)$$ is equal to

A
5
B
0
C
$$-$$3
D
1
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