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If (f:\mathbb{R}\to\mathbb{R}), (f(x)=\sqrt{(x+5)^2}), why is it not onto?यदि (f:\mathbb{R}\to\mathbb{R}), (f(x)=\sqrt{(x+5)^2}) है, तो यह आच्छादी क्यों नहीं है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Because negative values are not obtainedक्योंकि ऋणात्मक मान नहीं मिलते
Step 1: (\sqrt{(x+5)^2}=|x+5|) is always non-negative. Step 2: The codomain (\mathbb{R}) contains negative values, which are not obtained. Step 3: A function with a non-negative range is not onto the whole (\mathbb{R}).चरण 1: (\sqrt{(x+5)^2}=|x+5|) हमेशा अऋणात्मक होता है। चरण 2: सहप्रांत (\mathbb{R}) में ऋणात्मक मान हैं, जो फलन से नहीं मिलते। चरण 3: अऋणात्मक परास वाले फलन को पूरे (\mathbb{R}) पर आच्छादी नहीं मानें।
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