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If (f:\mathbb{R}\to\mathbb{R}), (f(x)=ax+b) where (a\ne0), what type of function is it?यदि (f:\mathbb{R}\to\mathbb{R}), (f(x)=ax+b) है जहाँ (a\ne0), तो फलन कैसा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Ontoआच्छादी
Step 1: Put (y=ax+b) and solve for (x). Step 2: (x=\frac{y-b}{a}) is real for every real (y) because (a\ne0). Step 3: A non-zero slope linear function from (\mathbb{R}) to (\mathbb{R}) is onto.चरण 1: (y=ax+b) मानकर (x) निकालें। चरण 2: (x=\frac{y-b}{a}) हर वास्तविक (y) के लिए वास्तविक है क्योंकि (a\ne0)। चरण 3: गैर-शून्य ढाल वाला रैखिक फलन (\mathbb{R}\to\mathbb{R}) पर आच्छादी होता है।
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