f(x) = 4x + 3 and its inverse f⁻¹(y) = (y − 3)/4f(x) = 4x + 3 और इसका प्रतिलोम f⁻¹(y) = (y − 3)/4f(x) = 4x + 3 aur iska inverse f⁻¹(y) = (y − 3)/4

NCERT Example 17 · Class 12 Maths · Chapter 1 · interactive diagram

Parts and what they mean

• x-axis (x-अक्ष) — The horizontal number line; inputs x are read here.
• y-axis (y-अक्ष) — The vertical number line; outputs y = f(x) are read here.
• Origin O(0, 0) (मूल बिंदु O(0, 0)) — Where the two axes cross.
• Points of f: (x, 4x + 3) (f के बिंदु: (x, 4x + 3)) — x = 1, 2, 3 give 7, 11, 15. Domain is N, so the graph is separate dots.
• Points of f⁻¹: (y, (y − 3)/4) (f⁻¹ के बिंदु: (y, (y − 3)/4)) — f⁻¹ sends 7 → 1, 11 → 2, 15 → 3: it undoes f.
• Line y = x (रेखा y = x) — Each point (a, b) of f has its mirror image (b, a) on f⁻¹.
• Mirror pairs (दर्पण युग्म) — (1, 7) ↔ (7, 1): swap x and y.

Original diagram drawn by Simple Learning Hub, based on NCERT Example 17. Report a mistake