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1
COMEDK 2024 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0

$$\text { Which of the following function is injective? }$$

A
$$ f(x)=x^2+2, x \in(-\infty, \infty) $$
B
$$ f(x)=|x+2|, x \in[-2, \infty) $$
C
$$ f(x)=\frac{4 x^2+3 x-5}{4+3 x-5 x^2}, x \in(-\infty, \infty) $$
D
$$ f(x)=(x-4)(x-5), x \in(-\infty, \infty) $$
2
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

Let $$f: R \rightarrow R$$ be a function defined by $$f=\frac{e^{|x|}-e^{-x}}{e^x+e^{-x}}$$ then

A
$$f$$ is an injection but not a surjection function
B
$$f$$ is a surjection but not an injection function
C
$$f$$ is neither an injection nor a surjection
D
$$f$$ is injection and surjection
3
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

Which of the following is not a homogenous function of $$x$$ and $$y$$

A
$$ \sin x-\cos y $$
B
$$ \cos ^2\left(\frac{y}{x}\right)+\frac{y}{x} $$
C
$$ x^2+2 x y $$
D
$$ 2 x-y $$
4
COMEDK 2023 Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $$2 f\left(x^2\right)+3 f\left(\frac{1}{x^2}\right)=x^2-1, \forall x \in R-\{0\}$$, then $$f\left(x^8\right)$$ is equal to

A
$$\frac{\left(1-x^8\right)\left(2 x^8+3\right)}{5 x^8}$$
B
$$\frac{\left(1+x^8\right)\left(2 x^8-3\right)}{5 x^8}$$
C
$$\frac{\left(1-x^8\right)\left(2 x^8-3\right)}{5 x^8}$$
D
None of these
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