Consider the following C function definition.int f(int x, int y) { for (int i=0; i<y; i++) { x=x+x+y; } return x; }Which of the following statements is/are TRUE about the above function?

In each iteration of the loop, the value of $x$ is updated as:

Adding $y$ to both sides gives a geometric progression:

After $y$ iterations (since the loop runs $y$ times):

Let us evaluate each option using this recurrence relation:

• (A) and (C) with $x = 20, y = 10$:

  $$\text{return value} = 2^{10}(20 + 10) - 10 = 30 \times 1024 - 10 = 30710$$

  Since $30710 < 2^{20} = 1048576$, statement (A) is FALSE. Since $30710 > 2^{10} = 1024$, statement (C) is FALSE.

• (B) with $x = 20, y = 20$:

  $$\text{return value} = 2^{20}(20 + 20) - 20 = 40 \times 2^{20} - 20$$

  Since $40 \times 2^{20} - 20 > 2^{20}$, statement (B) is TRUE.

• (D) with $x = 10, y = 20$:

  $$\text{return value} = 2^{20}(10 + 20) - 20 = 30 \times 2^{20} - 20$$

  Since $30 \times 2^{20} - 20 > 2^{20}$, statement (D) is TRUE.

Hence, the correct options are B and D.