Types Of Functions

We are given the functional equation:

2f(x)%20%2B%20f(1%20-%20x)%20%3D%20x%5E2

Step 1: Substitute

x%20%3D%201%20-%20x

Substitute

1%20-%20x

into the equation:

2f(1%20-%20x)%20%2B%20f(x)%20%3D%20(1%20-%20x)%5E2%20%3D%201%20-%202x%20%2B%20x%5E2

Step 2: Solve the system of equations Now, we have the following system of equations:

2f(x)%20%2B%20f(1%20-%20x)%20%3D%20x%5E2%20%5Cquad%20%5Ctext%7B(1)%7D

2f(1%20-%20x)%20%2B%20f(x)%20%3D%201%20-%202x%20%2B%20x%5E2%20%5Cquad%20%5Ctext%7B(2)%7D

Solve these equations to get:

f(x)%20%3D%20x%5E2%20%2B%202x%20-%201

Thus, the correct answer is

f(x)%20%3D%20x%5E2%20%2B%202x%20-%201

Chapter Questions
1 MCQs