Let f: R → R satisfy f(x + y) = f(x) + f(y) for all x, y in R. If f(1) = 7, then the value of f(4) is: A. 11 B. 28 C. 49 D. 7 Answer: B) 28 Explanation: Using the functional equation f(x+y) = f(x)+f(y), we get f(nx) = n f(x) for integer n. So, f(4) = 4 × f(1) = 4 × 7 = 28.

imo class 12 relations and functions

Let f: R → R satisfy f(x + y) = f(x) + f(y) for all x, y in R. If f(1) = 7, then the value of f(4) is:

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Let f: R → R satisfy f(x + y) = f(x) + f(y) for all x, y in R. If f(1) = 7, then the value of f(4) is:

Answer: B) 28

Explanation: Using the functional equation f(x+y) = f(x)+f(y), we get f(nx) = n f(x) for integer n. So, f(4) = 4 × f(1) = 4 × 7 = 28.

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