1
JEE Main 2024 (Online) 31st January Morning Shift
+4
-1

If $$f(x)=\frac{4 x+3}{6 x-4}, x \neq \frac{2}{3}$$ and $$(f \circ f)(x)=g(x)$$, where $$g: \mathbb{R}-\left\{\frac{2}{3}\right\} \rightarrow \mathbb{R}-\left\{\frac{2}{3}\right\}$$, then $$(g ogog)(4)$$ is equal to

A
$$-4$$
B
$$\frac{19}{20}$$
C
$$-\frac{19}{20}$$
D
4
2
JEE Main 2024 (Online) 30th January Evening Shift
+4
-1

If the domain of the function $$f(x)=\log _e\left(\frac{2 x+3}{4 x^2+x-3}\right)+\cos ^{-1}\left(\frac{2 x-1}{x+2}\right)$$ is $$(\alpha, \beta]$$, then the value of $$5 \beta-4 \alpha$$ is equal to

A
9
B
12
C
11
D
10
3
JEE Main 2024 (Online) 30th January Morning Shift
+4
-1

If the domain of the function $$f(x)=\cos ^{-1}\left(\frac{2-|x|}{4}\right)+\left\{\log _e(3-x)\right\}^{-1}$$ is $$[-\alpha, \beta)-\{\gamma\}$$, then $$\alpha+\beta+\gamma$$ is equal to :

A
11
B
12
C
9
D
8
4
JEE Main 2024 (Online) 29th January Morning Shift
+4
-1

If $$f(x)=\left\{\begin{array}{cc}2+2 x, & -1 \leq x < 0 \\ 1-\frac{x}{3}, & 0 \leq x \leq 3\end{array} ; g(x)=\left\{\begin{array}{cc}-x, & -3 \leq x \leq 0 \\ x, & 0 < x \leq 1\end{array}\right.\right.$$, then range of $$(f o g)(x)$$ is

A
$$[0,1)$$
B
$$[0,3)$$
C
$$(0,1]$$
D
$$[0,1]$$
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