For each of the following functions g(x) with a restricted domain:

i. State the range of g(x)

ii. Determine the equation of the inverse function g⁻¹(x)

iii. State the domain and range of g⁻¹(x)

iv. Sketch the graphs of y = g(x) and y = g⁻¹(x) on the same set of axes.

Transcribed Image Text:

1 a g(x) = \, {x ≤ R, x ≥ 3} 3 x - 2' e g(x) = x² + 2, {x ER, x > 2} c g(x) = {x € R, x > 2} b g(x) = 2x - 1, {x € R, x ≥ 0} d g(x)=√x - 3, {x € R, x ≥ 7} f g(x)= x³ - 8, {x € R, x ≥ 2}