Question

If f(x) = ax + b, where a and b are integers, f(-1) = -5 and f(3) = 3 then a and b are respectively

• A. 0, 2
• B. -3, -1
• C. 2, 3
• D. 2, -3

Hint:

When solving for unknowns in linear functions, substitute the known values of the function at specific points to form a system of equations. Solve the system to find the values of the constants.

Answer 1

The Correct Option is D

The correct answer is: (D): 2, -3

We are given the function \( f(x) = ax + b \), where \( a \) and \( b \) are integers. We also know that \( f(-1) = -5 \) and \( f(3) = 3 \). We are tasked with finding the values of \( a \) and \( b \).

Step 1: Use the information for \( f(-1) \)

Substitute \( x = -1 \) and \( f(-1) = -5 \) into the function \( f(x) = ax + b \):

f(-1) = a(-1) + b = -5

This simplifies to:

-a + b = -5

Step 2: Use the information for \( f(3) \)

Next, substitute \( x = 3 \) and \( f(3) = 3 \) into the function \( f(x) = ax + b \):

f(3) = a(3) + b = 3

This simplifies to:

3a + b = 3

Step 3: Solve the system of equations

We now have the system of equations:

-a + b = -5

3a + b = 3

To solve this system, subtract the first equation from the second equation:

(3a + b) - (-a + b) = 3 - (-5)

Simplifying this gives:

4a = 8

So, solving for \( a \), we get:

a = 2

Step 4: Solve for \( b \)

Substitute \( a = 2 \) into one of the original equations, say \( -a + b = -5 \):

-2 + b = -5

Solving for \( b \), we get:

b = -3

Conclusion:
The values of \( a \) and \( b \) are \( a = 2 \) and \( b = -3 \), so the correct answer is (D): 2, -3.