Consider the function f (x) = 9x. Which statement MUST be true? A) f (4) f (1) = f (8) f (5) B) f (4) ·f (1) = f (8) ·f (5) C) f (4) - f (1) = f (8) - f (5) D) f (4) - f (1) = f (-4) - f (-1)

Answer with Step-by-step explanation:

We are given that:

f (x) = 9x

A) f (4) f (1) = f (8) f (5)

f (4) f (1) = 9*4*9*1=324

f (8) f (5) = 9*8*9*5=3240

Hence, this option is incorrect

B) f (4) ·f (1) = f (8) ·f (5)

f (4) f (1) = 324

f (8) f (5) = 3240

Hence, this option is incorrect

C) f (4) - f (1) = f (8) - f (5)

f (4) - f (1) = 9*4-9=27

f (8) - f (5) = 9*8-9*5=27

Hence, this option is correct

D) f (4) - f (1) = f (-4) - f (-1)

f (4) - f (1) = 9*4-9=27

f (-4) - f (-1) = 9 * (-4) + 9=-27

Hence, this option is incorrect

Correct option is:

C) f (4) - f (1) = f (8) - f (5)

The correct answer is A

Step-by-step explanation:

Exponential functions grow by equal factors over equal intervals because the change in x is always the same as the exponent of the quotient of the values of y.