y = tan x on (−π/2, π/2) and y = tan⁻¹x(−π/2, π/2) पर y = tan x और y = tan⁻¹x(−π/2, π/2) par y = tan x aur y = tan⁻¹x

NCERT Fig 2.5 · Class 12 Maths · Chapter 2 · interactive diagram

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Parts and what they mean

y = \tan x on (-\pi/2, \pi/2) ((-\pi/2, \pi/2) पर y = \tan x) — Open interval: tan is not defined at \pm\pi/2. Here it is one-one and onto \mathbb{R}.
y = \tan^{-1} x (principal branch) (y = \tan^{-1} x (मुख्य शाखा)) — Domain \mathbb{R} (every real number), range (-\pi/2, \pi/2) — it never reaches \pm\pi/2.
Asymptotes x = \pm\pi/2 (अनंतस्पर्शी x = \pm\pi/2) — tan x shoots to \pm\infty near these lines.
Asymptotes y = \pm\pi/2 (अनंतस्पर्शी y = \pm\pi/2) — The mirror of x = \pm\pi/2: \tan^{-1}x comes close to them but never touches.
Mirror line y = x (दर्पण रेखा y = x) — Fold the paper along this line: the trig graph lands exactly on the inverse graph. A point (a, b) goes to (b, a).
Full graph (dashed, faint) (पूरा ग्राफ़ (धुँधला, डैश)) — The trig function on its natural domain — it is not one-one there.
A point and its mirror (एक बिंदु और उसका प्रतिबिंब) — (a, b) on tan ↔ (b, a) on \tan^{-1}.
(\pi/4, 1) on y = \tan x (y = \tan x पर (\pi/4, 1)) — Because \tan\frac{\pi}{4} = 1.
(1, \pi/4) on y = \tan^{-1}x (y = \tan^{-1}x पर (1, \pi/4)) — So \tan^{-1}1 = \frac{\pi}{4}.
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.

Original diagram drawn by Simple Learning Hub, based on NCERT Fig 2.5. Report a mistake