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If (f:\mathbb{R}\to \mathbb{R}), (f(x)=e^{x^2}), what is the correct statement?यदि (f:\mathbb{R}\to \mathbb{R}), (f(x)=e^{x^2}), तो सही कथन क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Not onto because range is ([1,\infty))आच्छादक नहीं है क्योंकि परास ([1,\infty)) है
Step 1: Since (x^2\ge0), (e^{x^2}\ge1). Step 2: The codomain (\mathbb{R}) contains (0) and negative values that are not obtained. Step 3: For exponential functions, the minimum of the exponent decides the range.चरण 1: (x^2\ge0) इसलिए (e^{x^2}\ge1)। चरण 2: सहक्षेत्र (\mathbb{R}) में (0) और ऋणात्मक मान हैं जो नहीं मिलते। चरण 3: घातीय फलन में घात का न्यूनतम मान परास तय करता है।
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