Question 5: Given that \(g(x)=ax+b+5\), where \(a\) and \(b\) are constant numbers. If \(g(-1)=0\) and \(g(2)=10\), find the values of \(a\) and \(b\).
Solution:
\(g(x)=ax+b+5\)
\(g(-1)=-a+b+5\)
\(-a+b+5=0\)\(\ \_\_\_\_\_\_\ (1)\)\(\quad \because g(-1)=0\)
\(g(2)=2a+b+5\)
\(2a+b+5=10\)\(\ \_\_\_\_\_\_\ (2)\)\(\quad \because g(2)=10\)
Subtracting equation \((1)\) from \((2)\), we have
\(\ \ 2a+b+5=10\)
\(\underline{\underset{+}{-}a\underset{-}{+}b\underset{-}{+}5=\underset{-}{}0}\)
\(\ \ 3a\ \ \ \ \ \ \ \ \ \ \ \ \ \ =10\)
\(a=\large{\frac{10}{3}}\)
Put value of \(a\) in equation \((1)\), we have
\(-\large{\frac{10}{3}}+b+5=0\)
\(b=\large{\frac{10}{3}}-5\)
\(b=\large{\frac{10-15}{3}}\)
\(b=-\large{\frac{5}{3}}\)