Need help findind function such as $f(a) = c$ and $f(c) = a$ I haven't practiced algebra for ages and it seems I have issues with basic algebraic problem. So I need to find a function such as $f(a) = c$ and $f(c) = a$
As I understand we can do it with the function of a line. E.g
$$ c = ma + b$$ 
$$ a = mc + b$$
But now I am confused on what to do next. I need to solve for $m$ and $b$ right?
$$c - a = ma - mc$$
$$c - a = m(a - c)$$
$$m = \frac{c - a}{a - c}$$
And then $b$
$$c = \frac{c - a}{a - c} \times a + b$$
$$b = c - \frac{c - a}{a - c} \times a$$
And now I am stuck. What should I do next?

$$f(x)=c \frac{x-c}{a-c}+a \frac{x-a}{c-a}$$ should do the job.
You're right that a linear function will work. But then you should look at a general linear function $y=ux+v$ and write $$\begin{cases} c=ua+v\\
a=uc+v
\end{cases}$$ and solve the system to find $(u,v)$.
