Question

if f(x)=ax+b,f(-1)=-1and f(3)=1, find 'a' and 'b'​

Answer 1

ANSWER:

Given:

• f(x) = ax + b
• f(-1) = -1
• f(3) = 1

To Find:

• Value of a and b

Solution:

We are given that,

⇒ f(x) = ax + b

Putting x = -1,

⇒ f(-1) = a(-1) + b

As f(-1) = -1,

⇒ -1 = -a + b

⇒ b - a = -1 --------(1)

Now, on putting x = 3,

⇒ f(3) = a(3) + b

As f(3) = 1

⇒ 1 = 3a + b

⇒ 3a + b = 1 --------(2)

Subtracting (1) from (2),

⇒ (3a + b) - (b - a) = 1 - (-1)

⇒ 3a + b - b + a = 1 + 1

⇒ 4a = 2

⇒ a = 2/4

⇒ a = 1/2

Putting value of a in (1),

⇒ b - a = -1

⇒ b - (1/2) = -1

Transposing 1/2 to RHS,

⇒ b = -1 + 1/2

⇒ b = -1/2

Hence, value of a is 1/2 and value of b is -1/2.