The function \( f(x)=m x \) satisfies \( f(x+y)=f(x)+f(y) \) and \( f(x)=a^{x} \) satisfies \( f....

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The function \( f(x)=m x \) satisfies \( f(x+y)=f(x)+f(y) \) and \( f(x)=a^{x} \) satisfies \( f(x+y)=f(x) f(y) \). From the given functional relations, we can determine several things about the functions. At times the function can be determined uniquely from the functional equation.
If \( f(x+y)=f(x)+f(y) \) for all \( x, y \) and \( f(1)=1 \) then \( f(-9 / 8) \) is equal to
(1) \( 9 / 8 \)
(2) \( 8 / 9 \)
(3) \( -9 / 8 \)
(4) 1


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