Answer:

f(x) = √2x - 4

Domain: x ∈ [2, +∞⟩

≈ x ≥ 2

Range: f(x) ∈ [0, +∞⟩

y = √2, when x = 3

y = 2, when x = 4

y = √6, when x = 5

y = √8, when x = 6

y = √10, when x = 7

To find the inverse, substitute f(x) as y.

y = √2x - 4

Interchange the variables.

x = √2y - 4

Swap the sides.

√2y - 4 = x

Square both sides of the equation.

2y - 4 = x²

Move -4 to the right-hand side and change its sign.

2y = x² + 4

Divide both sides by 2.

y = ½x² + 2

Substitute y as f^-1(x).

f^-1(x) = ½x² + 2

Inverse: ½x² + 2

Domain: x ∈ R

Range: f^-1(x) ∈ [2, +∞⟩

y = 13/2, when x = 3

y = 10, when x = 4

y = 29/2, when x = 5

y = 20, when x = 6

y = 53/2, when x = 7