If $g(x) = x^2 + x - 2$ and $\frac{1}{2} (g \circ f)(x) = 2x^2 - 5x + 2$,then $f(x)$ is equal to:

Show that if $f: A \rightarrow B$ and $g: B \rightarrow C$ are onto,then $g \circ f: A \rightarrow C$ is also onto.

If $f(x) = \begin{cases} 2+2x, & -1 \leq x < 0 \\ 1-\frac{x}{3}, & 0 \leq x \leq 3 \end{cases}$ and $g(x) = \begin{cases} -x, & -3 \leq x \leq 0 \\ x, & 0 < x \leq 1 \end{cases}$,then the range of $(f \circ g)(x)$ is:

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

Let $f(x) = 1 - x$,$g(x) = \frac{1}{1 - x}$,and $h(x) = \frac{1}{x}$ be three functions,for $x \neq 0, 1$. If a function $F(x)$ satisfies $f(F(h(x))) = g(x)$,then which of the following is true?

If $f: R \rightarrow R$ and $g: R \rightarrow R$ are defined by $f(x)=x-[x]$ and $g(x)=[x]$ for $x \in R$,where $[x]$ is the greatest integer not exceeding $x$,then for every $x \in R, f(g(x))$ is equal to