JEE Main 2024 (Online) 1st February Evening Shift | Functions Question 14 | Mathematics

If the domain of the function

$f(x)=\frac{\sqrt{x^2-25}}{\left(4-x^2\right)}+\log _{10}\left(x^2+2 x-15\right)$ is $(-\infty, \alpha) \cup[\beta, \infty)$, then $\alpha^2+\beta^3$ is equal to :

140

175

125

150

JEE Main 2024 (Online) 1st February Morning Shift

MCQ (Single Correct Answer)

-1

Let $f: \mathbf{R} \rightarrow \mathbf{R}$ and $g: \mathbf{R} \rightarrow \mathbf{R}$ be defined as

$f(x)=\left\{\begin{array}{ll}\log _{\mathrm{e}} x, & x>0 \\ \mathrm{e}^{-x}, & x \leq 0\end{array}\right.$ and

$g(x)=\left\{\begin{array}{ll}x, & x \geqslant 0 \\ \mathrm{e}^x, & x<0\end{array}\right.$. Then, gof : $\mathbf{R} \rightarrow \mathbf{R}$ is :

one-one but not onto

neither one-one nor onto

onto but not one-one

both one-one and onto

JEE Main 2024 (Online) 31st January Morning Shift

MCQ (Single Correct Answer)

-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

$$-4$$

$$\frac{19}{20}$$

$$-\frac{19}{20}$$

JEE Main 2024 (Online) 30th January Evening Shift

MCQ (Single Correct Answer)

-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