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फलन (f(x)=|2x-8|+3) का शीर्ष कौन सा है?
What is the vertex of (f(x)=|2x-8|+3)?
#standard-functions
#modulus-graph
#vertex-linear-inside
A ((4,3))
B ((-4,3))
C ((8,3))
D ((4,-3))
Explanation opens after your attempt
Correct Answer
A. ((4,3))
Step 1
Concept
For the vertex, set (2x-8=0), which gives (x=4). The outside (+3) makes the vertex ((4,3)).
Step 2
Why this answer is correct
The correct answer is A. ((4,3)). For the vertex, set (2x-8=0), which gives (x=4). The outside (+3) makes the vertex ((4,3)).
Step 3
Exam Tip
शीर्ष के लिए (2x-8=0) रखें जिससे (x=4) मिलता है। बाहर (+3) होने से शीर्ष ((4,3)) है।
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फलन \(f:\mathbb{R}\to\mathbb{R}\), (f(x)=|2x+1|) के लिए सही विकल्प चुनिए।
Choose the correct option for \(f:\mathbb{R}\to\mathbb{R}\), (f(x)=|2x+1|).
#relations-functions
#one-one-function
#absolute-value
#linear-inside
A एकैकी है / It is one-one
B एकैकी नहीं है / It is not one-one
C रैखिक है / It is linear
D स्थिर है / It is constant
Explanation opens after your attempt
Correct Answer
B. एकैकी नहीं है / It is not one-one
Step 1
Concept
Due to absolute value, two different inputs can give the same positive value.
Step 2
Why this answer is correct
(f(0)=1) and (f(-1)=1), while \(0\neq -1\).
Step 3
Exam Tip
Check absolute value functions carefully on all of \(\mathbb{R}\). चरण 1: निरपेक्ष मान के कारण दो अलग आगत समान धनात्मक मान दे सकते हैं। चरण 2: (f(0)=1) और (f(-1)=1), जबकि \(0\neq -1\)। चरण 3: निरपेक्ष मान वाले फलन को पूरे \(\mathbb{R}\) पर सावधानी से जाँचें।
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