Answer:
a = 3, b = - 2
Step-by-step explanation:
Given f(1) = 1 and f(2) = 5, that is
substitute x = 1 and equate to 1, substitute x = 2 and equate to 5
a + b = 1 → (1)
2a + [tex]\frac{b}{2}[/tex] = 5 → (2)
Multiplying (1) by - 2 and adding to (2) will eliminate a
- 2a - 2b = - 2 → (3)
Add (2) and (3) term by term to eliminate a
0 - [tex]\frac{3}{2}[/tex] b = 3
- [tex]\frac{3}{2}[/tex] b = 3 ( multiply both sides by - [tex]\frac{2}{3}[/tex] )
b = - 2
Substitute b = - 2 into (1)
a - 2 = 1 ( add 2 to both sides )
a = 3
Then a = 3 and b = - 2
