If (p(x)=10x+a) and (p(p(0))=110), what is the value of (a)?
Answer and explanation
Correct answer: 10
First, \(p(0)=10\times 0+a=a\). Hence, \(p(p(0))=p(a)=10a+a=11a\). Given \(11a=110\), we get \(a=10\). Option 11 may result from incorrectly taking the coefficient in \(p(a)=11a\) as the value of \(a\). Exam tip: In a composite function, evaluate the inner function first.
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
First, \(p(0)=10\times 0+a=a\). Hence, \(p(p(0))=p(a)=10a+a=11a\). Given \(11a=110\), we get \(a=10\). Option 11 may result from incorrectly taking the coefficient in \(p(a)=11a\) as the value of \(a\). 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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