Question 22.
Suppose f(x, y) is a real-valued function such that f(3x + 2y, 2x − 5y) = 19x, for all real numbers x and y. The value of x for which f(x, 2x) = 27, is
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Given that f(3x + 2y, 2x - 5y) = 19x.
Let us assume the function f(a, b) is a linear combination of a and b.
=> f(3x+2y, 2x-5y) = m(3x+2y) + n(2x-5y) = 19x
=> 3m + 2n = 19 and 2m - 5n = 0
Solving we get m = 5 and n = 2
=> f(a, b) = 5a+2b
=> f(x, 2x) = 5x + 2(2x) = 9x = 27 => x = 3.
