Relations, Functions and Graphs I

$f(5) = 4(5) - 1 = 20 - 1 = 19$. Replace every $x$ with 5.

The domain is the set of first coordinates (the inputs); the range is the set of second coordinates (the outputs).

$f(-2) = 7 - 3(-2) = 7 + 6 = 13$. Multiplying $-3$ by $-2$ gives $+6$.

Apply $g$ first: $g(x) = 2x$. Then $f(2x) = 2x + 4$.

From $y = \dfrac{x-1}{2}$, multiply by 2 to get $2y = x - 1$, then add 1: $x = 2y+1$. Check: $f(7) = 3$ and $f^{-1}(3) = 7$ ✓

A function requires every input to have exactly one output. Repeated outputs are allowed, but a repeated input with different outputs is not.