Question

the function f satisfies the functional equation 3f(x)+2f(x+59/x-1)=10x+30 for all x not equal to 0 ,the value of f(7).

Answer 1

Replace x with 1-x→ f(1-x) - 2f(x) = (1-x)² + 2 Multiplying with 2 on both sides 2f(1-x) - 4f(x) = 2(1-x)² + 4.

Given equation. f(x) - 2f(1-x) = x² + 2 Adding equations 1 and 2, f(1-x) gets eliminated.

Therefore, -3f(x) = 2 - 4x + 2x² + 4 + x² + 2 -3f(x) = 3x² - 4x + 8. So the final function is f (7) =−3x2−4x+83.

Answer 2

Answer:

f(7) =4

Step-by-step explanation:

See the attachment.

I hope you are satisfied by my answer.