If f(3x - y, x + y) = x^2 y, then f(3, 2) is equal to?

The value of f ( 3 , 2 ) is 64 75 ​ after solving the system of equations derived from the original function definition. This was achieved by substituting the values of x and y that satisfy the conditions for the function. Finally, the function was evaluated to find the desired output.
;

Answered by Anonymous | 2025-07-04

To solve the problem where f ( 3 x − y , x + y ) = x 2 y , and we need to find f ( 3 , 2 ) , we should first understand how the function f operates.
Given f ( 3 x − y , x + y ) = x 2 y , let's determine the expressions in the parentheses:

First Argument of f : 3 x − y

Second Argument of f : x + y


To solve for f ( 3 , 2 ) , we need to find values of x and y such that:
3 x − y = 3 x + y = 2
We can solve these two linear equations as follows:

From x + y = 2 , express y as: y = 2 − x

Substitute y = 2 − x into the equation 3 x − y = 3 :
3 x − ( 2 − x ) = 3 3 x − 2 + x = 3 4 x − 2 = 3 4 x = 5 x = 4 5 ​

Now substitute x = 4 5 ​ back to find y :
y = 2 − 4 5 ​ y = 4 8 ​ − 4 5 ​ y = 4 3 ​


Therefore, x = 4 5 ​ and y = 4 3 ​ .
Substitute these values into x 2 y :
x 2 y = ( 4 5 ​ ) 2 × 4 3 ​ = 16 25 ​ × 4 3 ​ = 64 75 ​
Thus, f ( 3 , 2 ) is 64 75 ​ .

Answered by OliviaLunaGracy | 2025-07-06