Question

If f (x) = ax + b, where a and b are integers, f (–1) = – 5 and f (3) = 3, then a and b are equal to 

A. a = – 3, b = –1  

B. a = 2, b = – 3 

C. a = 0, b = 2 

D. a = 2, b = 3

Answer 1

Given: f (x) = ax + b, where a and b are integers, f (–1) = – 5 and f (3) = 3

To find: the values of a and b

Explanation: we have f (x) = ax + b

Put x = -1 in above equation we get

f (-1) = a(-1) + b

But it is also given f(-1) = -5, so above equation becomes

-5 = -a + b

⇒ b = a-5………(i)

we have f (x) = ax + b

Put x = 3 in above equation we get

f (3) = a(3) + b

But it is also given f(3) = 3, so above equation becomes

3 = 3a + b

Now substituting the value of b from equation (i), we get

3 = 3a + a-5

⇒ 4a = 5 + 3

⇒ 4a = 8

⇒ a = 2

Substituting the value of a in equation (i), we get

b = a-5 = 2-5 = -3

Hence the values of a and b are 2 and -3 respectively.

Hence the correct answer is option (B)