(i) $g(x) = 5 - x$

(i) $g(x) = 5 - x$

Given:

• Domain ($D_g$): Any real number can be substituted for $x$:

  • $g(0) = 5 - 0 = 5$
  • $g(2) = 5 - 2 = 3$
  • $g(-3) = 5 - (-3) = 8$ No division by zero and no negative square roots:
  $$\boxed{D_g = \mathbb{R} = (-\infty, \infty)}$$

• Range ($R_g$): Let $y = 5 - x \iff x = 5 - y$. Any real output can be obtained by choosing $x = 5 - y$:

  • For $y = 10 \implies x = 5 - 10 = -5 \implies g(-5) = 10$
  • For $y = 0 \implies x = 5 - 0 = 5 \implies g(5) = 0$
  $$\boxed{R_g = \mathbb{R} = (-\infty, \infty)}$$