Additional Mathematics – Functions | e-Consult

Answer 2

1. Choose three convenient points on g(x): (0,3), (1,5), (‑2,‑1). Plot and join them to obtain a straight line with slope 2.
2. To obtain the inverse, solve y = 2x + 3 for x: x = (y ‑ 3)/2, so g^‑1(x) = (x ‑ 3)/2.
3. Plot the inverse using swapped coordinates: (3,0), (5,1), (‑1,‑2). Connect these points; the line has slope ½ and y‑intercept ‑3/2.
4. Draw the line y = x. Each point of g(x) reflects across this line to the corresponding point of g^‑1(x). The two lines are mirror images about y = x, confirming the relationship.