Q9 of 82 Page 126

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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