1
COMEDK 2024 Morning Shift
+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
2
COMEDK 2024 Morning Shift
+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
$$2 x-y$$
3
COMEDK 2023 Morning Shift
+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
4
COMEDK 2023 Evening Shift
+1
-0

The range of $$x$$ which satisfy the inequation : $$-5 \leq \frac{2-3 x}{4} \leq 9$$ is

A
$$\left(-\frac{34}{3},-\frac{22}{3}\right)$$
B
$$\left[-\frac{34}{3}, \frac{22}{3}\right)$$
C
$$\left[-\frac{34}{3}, 8\right]$$
D
$$\left[-\frac{34}{3}, \frac{22}{3}\right]$$
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