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If (f:\mathbb{R}\to\mathbb{R}) is defined by (f(x)=2x+3) and (g:\mathbb{R}\to\mathbb{R}) by (g(x)=\frac{x-3}{2}), which statement is correct?यदि (f:\mathbb{R}\to\mathbb{R}) को (f(x)=2x+3) और (g:\mathbb{R}\to\mathbb{R}) को (g(x)=\frac{x-3}{2}) से परिभाषित किया गया है, तो सही कथन कौन सा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (g=f^{-1})(g=f^{-1})
Step 1: (g(f(x))=g(2x+3)=\frac{2x+3-3}{2}=x). Step 2: (f(g(x))=2\cdot\frac{x-3}{2}+3=x). Step 3: If both compositions give the identity function, the two functions are inverses.चरण 1: (g(f(x))=g(2x+3)=\frac{2x+3-3}{2}=x)। चरण 2: (f(g(x))=2\cdot\frac{x-3}{2}+3=x)। चरण 3: दोनों संयोजन पहचान फलन दें, तो दोनों फलन परस्पर व्युत्क्रम होते हैं।
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