New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Functions question

2025 · 23 Jan · Shift 1 · Q29

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Functions
2025 · 23 Jan · Shift 1 · Q29

Functions question

2025 · 23 Jan · Shift 1 · Q29

JEE MainMathematicsFunctionsMCQ+4 / −1

Let

f(x)=\log _{\mathrm{e}} x

and

g(x)=\frac{x^4-2 x^3+3 x^2-2 x+2}{2 x^2-2 x+1}

. Then the domain of

f \circ g

is

A
$(0, \infty)$
B
$[1, \infty)$
C
$\mathbb{R}$
D
$[0, \infty)$

More from Functions

Let $f (x) = \frac{2 ^{x + 2} + 16}{2 ^{2 x + 1} + 2 ^{x + 4} + 32}$ . Then the value of $8 (f (\frac{1}{15}) + f (\frac{2}{15}) + \dots + f (\frac{59}{15}))$ is equal to2025 · MCQ
The function $f : (- \infty, \infty) \to (- \infty, 1)$ , defined by $f (x) = \frac{2 ^{x} - 2 ^{- x}}{2 ^{x} + 2 ^{- x}}$ is :2025 · MCQ
If $f (x) = \frac{2 ^{x}}{2 ^{x} + 2}, x \in R$ , then $\sum_{k = 1}^{81} f (\frac{k}{82})$ is equal to2025 · MCQ
Let $f : R \to R$ be a function defined by $f (x) = (2 + 3 a) x^{2} + (\frac{a + 2}{a - 1}) x + b, a e q 1$ . If $f (x + y) = f (x) + f (y) + 1 - \frac{2}{7} x y$ , then the value of $28 i = 1 \sum 5 ∣ f (i) ∣$ is2025 · MCQ
Let $f : [0, 3] \to$ A be defined by $f (x) = 2 x^{3} - 15 x^{2} + 36 x + 7$ and $g : [0, \infty) \to B$ be defined by $g (x) = \frac{x ^{2025}}{x ^{2025} + 1}$ , If both the functions are onto and $S = {x \in Z; x \in A$ or $x \in B}$ , then $n (S)$ …2025 · MCQ
If the domain of the function $lo g_{5} (18 x - x^{2} - 77)$ is $lo g_{(x - 1)} (\frac{2 x ^{2} + 3 x - 2}{x ^{2} - 3 x - 4})$ and the domain of the function $lo g_{(x - 1)} (\frac{2 x ^{2} + 3 x - 2}{x ^{2} - 3 x - 4})$ is $α^{2} + β^{2} + γ^{2}$ , then $α^{2} + β^{2} + γ^{2}$ is…2025 · MCQ
Let $f : R \to R$ and $g : R \to R$ be defined as $f (x) = {lo g_{e} x, e^{- x}, x > 0 x \leq 0$ and $g (x) = {x, e^{x}, x ⩾ 0 x < 0$ …2024 · MCQ
If the domain of the function $f (x) = \frac{x ^{2} - 25}{( 4 - x ^{2} )} + lo g_{10} (x^{2} + 2 x - 15)$ is $(- \infty, α) \cup [β, \infty)$ , then $α^{2} + β^{3}$ is equal to :2024 · MCQ