f(x) = x²: neither one-one nor ontof(x) = x²: न एकैकी, न आच्छादकf(x) = x²: na one-one, na onto

NCERT Fig 1.4 · 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.
• Graph of f(x) = x² (f(x) = x² का ग्राफ़) — A parabola opening upward; it never goes below the x-axis.
• Line y = 1 meets twice (रेखा y = 1 दो बार काटती है) — f(−1) = 1 = f(1) but −1 ≠ 1, so f is not one-one.
• Points (−1, 1) and (1, 1) (बिंदु (−1, 1) और (1, 1)) — Two different inputs, same output 1.
• Line y = −2 never meets (रेखा y = −2 कभी नहीं काटती) — x² = −2 has no real solution, so −2 in the co-domain R is not an image: f is not onto.

Original diagram drawn by Simple Learning Hub, based on NCERT Fig 1.4. Report a mistake