Question

Let $f : \mathbb{R}^2 	o \mathbb{R}$ be a real-valued function defined as $f(0, y) = y + 1$ and $f(x + 1, y) = f(x, f(x, y)) + x$. What is the value of $f(2, 2)$?

Accepted Answer

B. Given $f(0, y) = y + 1$. First find $f(1, y)$: $f(1, y) = f(0, f(0, y)) + 0 = f(0, y + 1) + 0 = (y + 1) + 1 = y + 2$. Now find $f(2, y)$: $f(2, y) = f(1, f(1, y)) + 1 = f(1, y + 2) + 1 = (y + 2 + 2) + 1 = y + 5$. For $y = 2$: $f(2, 2) = 2 + 5 = 7$.

Real-valued function f(2, 2)

Explanation

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