# If f(x) = ax + b and f(0) = 3, f(2) = 5, then let us determine the values of a and b.

We have,

f(x) = ax + b …(i)

f(0) = 3

f(2) = 5

Replace x by 0 in equation (i), we get

f(0) = a(0) + b

3 = 0 + b [ f(0) = 3]

3 = b

b = 3

Replace x by 2 in equation (i), we get

f(2) = a(2) + b

5 = 2a + b [ f(2) = 5]

5 = 2a + 3 [ b = 3]

2a = 5 – 3

2a = 2

a = 1

Thus, a = 1 and b = 3.

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