I saw an exam question using this notation:
$$x^2\,f(x) = x^2 + 7x + 3\,.$$
I didn't understand it, so I checked the answer and I saw that was equal to:
$$f(x) = \frac{x^2 + 7x + 3}{x^2}\,.$$
Is the former a common function notation? Where or how can I find more information about it?
Thanks in advance.
Assuming you have copied it verbatim, it's a simple redistribution of terms. Suppose for example that you wanted to subtract 3 from both sides. You would then have $$x^2 f(x) - 3 = x^2 + 7x.$$
That was just for the sake of example. Let's go back to $$x^2 f(x) = x^2 + 7x + 3.$$ Now we want to divide both sides by $x^2$. Then we have $$\frac{x^2 f(x)}{x^2} = \frac{x^2 + 7x + 3}{x^2}$$ $$\frac{x^2}{x^2} f(x) = \frac{x^2 + 7x + 3}{x^2}.$$ As we're assuming $x \neq 0$, it follows that $$\frac{x^2}{x^2} = 1,$$ and so $$1 f(x) = \frac{x^2 + 7x + 3}{x^2}$$ $$f(x) = \frac{x^2 + 7x + 3}{x^2}.$$