Let $f(x) = \sin x$ and $g(x) = \cos x$. Which of the following statements is false?

If $f: R \rightarrow R$ and $g: R \rightarrow R$ are defined by $f(x)=2x+3$ and $g(x)=x^2+7$, then the values of $x$ such that $g(f(x))=8$ are

Consider functions $f: A \rightarrow B$ and $g: B \rightarrow C$ $(A, B, C \subseteq \mathbb{R})$ such that $(g \circ f)^{-1}$ exists. Then:

Give examples of two functions $f: N \rightarrow N$ and $g: N \rightarrow N$ such that $g \circ f$ is onto but $f$ is not onto.

If $f$ is an increasing function and $g$ is a decreasing function, and $fog$ is defined, then what kind of function is $fog$?

Let $f : R \rightarrow R$ and $g : R \rightarrow R$ be defined as $f(x) = \begin{cases} x+a, & x < 0 \\ |x-1|, & x \geq 0 \end{cases}$ and $g(x) = \begin{cases} x+1, & x < 0 \\ (x-1)^2+b, & x \geq 0 \end{cases}$ where $a, b$ are non-negative real numbers. If $(g \circ f)(x)$ is continuous for all $x \in R$,then $a+b$ is equal to ......