Given f(x) = ax + b/x,
f(1) = 1, and f(2)= 5, find constants a and b

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 + = 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 - b = 3

- b = 3 ( multiply both sides by - )

b = - 2

Substitute b = - 2 into (1)

a - 2 = 1 ( add 2 to both sides )

a = 3

Then a = 3 and b = - 2

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step-by-step explanation:

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