Condition for Monotonically Increasing Function

Q. Let $f,g:R\to R$ be defined by $f\left(x\right)=x^2-\frac{\cos x}{2}$ and $g\left(x\right)=\frac{x\sin x}{2}$. Then

1. $f\left(x\right)=g\left(x\right)$ has exactly one solution.
2. $f\left(x\right)=g\left(x\right)$ has exactly two solutions.
3. $f\left(x\right)-g\left(x\right)\to \infty$ as $x\to -\infty$
4. The minimum value of $f\left(g\right(x\left)\right)$ is $-1.$

Q.

Which of the following function is a monotonically increasing function?

1. $f\left(x\right)=x^2+2x$

2. $f\left(x\right)=x^3+2x$

3. $f\left(x\right)=x^3+2x$

4. $f\left(x\right)=cosx$

Q. Let $f\left(x\right)=\frac{x}{\sqrt{a^2+x^2}}-\frac{d-x}{\sqrt{b^2+(d-x{)}^2}},x\in R$,

where $a,b$ and $d$ are non-zero real constants, then :

1. $f$ is an increasing function of $x$
2. $f$ is neither increasing nor decreasing function of $x$
3. $f$ is a decreasing function of $x$
4. $f^{\prime }$ is not a continuous function of $x$