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If (p(x)=x+a) and (p(p(3))=13), what is the value of (a)?
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Answer and explanation
Correct answer: 5
Given \(p(x)=x+a\), we get \(p(3)=3+a\). Therefore, \(p(p(3))=p(3+a)=(3+a)+a=3+2a\). Hence \(3+2a=13\), so \(2a=10\) and \(a=5\). Option 10 may result from stopping at \(2a=10\) without dividing by 2. Exam tip: In a composite function, evaluate the inner function first.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
Given \(p(x)=x+a\), we get \(p(3)=3+a\). Therefore, \(p(p(3))=p(3+a)=(3+a)+a=3+2a\). Hence \(3+2a=13\), so \(2a=10\) and \(a=5\). Option 10 may result from stopping at \(2a=10\) without dividing by 2. Exam tip: In a composite function, evaluate the inner function first.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Introduction to Polynomials. Topic: Linear polynomials.
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