Question

If f(x)= ax+b, f(2)= 5 and f(3)= 7, find the value of a and b and f(x). with clear process​

Answer 1

Given :

f(x) = ax + b

f(2) = 5

f(3) = 7

Solution :

f(x) = ax + b  . . . (1)

f(2) = 5

Thus from equation (1),

f(x) = 5a + b  . . . (2)

Now,

f(3) = 7

Thus from equation (1),

f(x) = 7a + b  . . . (3)

Now subtracting equation (3) from (2),

f(x) = ( 7a + b) - ( 5a + b)

f(x) = 2a  . . . (4)

Now put this value of f(x) in equation (2) we get,

2a = 5a + b  . . . (5)

b = 2a - 5a

b = -3a  . . . (6)

Putting this value in equation (5) we get,

2a = 5a - 3a

2a = 2a

a = 1

Thus from equation (6),

b = -3

Since, for finding f(x),

f(x) = ax + b

f(x) = (1)x + (-3)

f(x) = x - 3