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Consider the function f(x) = 3^x. Which statement MUST be true?

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Consider the function f(x) = 3^x. Which statement MUST be true?

Consider the function f(x) = 3^x. Which statement MUST be true?
A) f(3)/f(1) = f(6)/f(4)
B) f(3)·f(1) = f(6)·f(4)
C) f(3) – f(1) = f(6) – f(4)
D) f(3) – f(1) = f(-3) – f(-1)




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    1. Quizzma Team

      To analyze the function ( f(x) = 3^x ), let’s evaluate each statement:

      A) ( f(3)/f(1) = f(6)/f(4) )

      Calculating both sides:

      – ( f(3) = 3^3 = 27 )

      – ( f(1) = 3^1 = 3 )

      – ( f(6) = 3^6 = 729 )

      – ( f(4) = 3^4 = 81 )

      So, left side ( = frac{27}{3} = 9 ) and right side ( = frac{729}{81} = 9 ). This statement is true.

      B) ( f(3) cdot f(1) = f(6) cdot f(4) )

      Calculating both sides:

      – ( f(3) cdot f(1) = 27 cdot 3 = 81 )

      – ( f(6) cdot f(4) = 729 cdot 81 )

      Since ( 729 cdot 81 ) is much larger than 81, this statement is not true.

      C) ( f(3) – f(1) = f(6) – f(4) )

      Calculating both sides:

      – Left side: ( 27 – 3 = 24

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