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If (f:\mathbb{R}-{1}\to\mathbb{R}-{2}) and (f(x)=\frac{2x+3}{x-1}), which statement is correct?यदि (f:\mathbb{R}-{1}\to\mathbb{R}-{2}) तथा (f(x)=\frac{2x+3}{x-1}) हो तो सही कथन कौन सा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: The function is one-one and ontoफलन एकैकी और आच्छादी है
Step 1: From (y=\frac{2x+3}{x-1}), we get (x=\frac{y+3}{y-2}). Step 2: For every (y\neq2), exactly one (x) is obtained. Step 3: Therefore with codomain (\mathbb{R}-{2}), the function is bijective.चरण 1: (y=\frac{2x+3}{x-1}) से (x=\frac{y+3}{y-2}) मिलता है। चरण 2: (y=2) को छोड़कर हर (y) के लिए ठीक एक (x) मिलता है। चरण 3: इसलिए दिए गए सहप्रांत (\mathbb{R}-{2}) में फलन द्वैकीय है।
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