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

1.	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» 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)

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»

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)