Q. 94.9( 10 Votes )

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

Answer :

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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