I would like help with this exercise. Thanks in advance.
A function $g: ℝ\toℝ$ satisfies $g(g(x))=x$ for all $x\inℝ$.
a) Show that $g$ is injective.
Let $a\inℝ$ and $b\inℝ$. Then,
$$g(a)=g(b)$$ $$g(g(a))=g(g(b))$$ $$a=b$$
b) If $(3,4)$ is a point on the graph of $g$ find $g(4)$.
$$g(3)=4$$ $$g(g(3))=g(4)$$ $$3=g(4)$$
c) Show that $g$ is surjective.
How do I prove it is surjective?
Are parts (a) and (b) ok?
a) b) are fine. If $x$ is any real number then $y=g(x)$ is a real number such that $g(y)=x$. Hence, $g$ is surjective.