Question
Download Solution PDFComprehension
Let f = {(1, 1), (2, 4), (3, 7), (4, 10)}
If f(x) = px + q then what is the value of (p + q) ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation:
Given,
The function is \(f = \{(1, 1), (2, 4), (3, 7), (4, 10)\} \), and we are also given that the function is \( f(x) = px + q \), where p and q are constants.
Using the points f(1) = 1 and f(2) = 4 , we create the following system of equations:
- From f(1) = 1 , we have \(p(1) + q = 1 \), so p + q = 1 .......(1).
- From f(2) = 4 , we have p(2) + q = 4 , so 2p + q = 4 ..........( 2).
Subtract Equation 1 from Equation 2:
\( (2p + q) - (p + q) = 4 - 1 \)
\( p = 3 \)
Now, substitute p = 3 into Equation 1:
\( 3 + q = 1 \)
\( q = -2 \)
\( p + q = 3 + (-2) = 1 \)
∴ The value of p + q is 1.
The correct answer is Option (3).
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