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If (f:[0,\frac{\pi}{4}]\to\mathbb{R}), (f(x)=\tan x), why is it not onto?यदि (f:[0,\frac{\pi}{4}]\to\mathbb{R}), (f(x)=\tan x) है, तो यह आच्छादी क्यों नहीं है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Because its range is only ([0,1])क्योंकि इसका परास केवल ([0,1]) है
Step 1: On ([0,\frac{\pi}{4}]), (\tan x) takes values from (0) to (1). Step 2: The codomain (\mathbb{R}) contains values such as (2), which are not in the range. Step 3: A small range cannot cover a larger codomain.चरण 1: ([0,\frac{\pi}{4}]) पर (\tan x) (0) से (1) तक मान लेता है। चरण 2: सहप्रांत (\mathbb{R}) में (2) जैसे मान भी हैं, जो परास में नहीं आते। चरण 3: बड़े सहप्रांत के सामने छोटा परास आच्छादीपन नहीं देता।
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