How are the functions f (x) = 16^x and g (x) = 16^ (1/2) x related? The output values of g (x) are one-half the output values of f (x) for the same value of x. The output values of g (x) are one-quarter the output values of f (x) for the same value of x. The output values of g (x) are the square root of the output values of f (x) for the same value of x. The output values of g (x) are the square of the output values of f (x) for the same value of x.

Question

Mathematics

Blaze Malone

24 September, 18:20

How are the functions f (x) = 16^x and g (x) = 16^ (1/2) x related? The output values of g (x) are one-half the output values of f (x) for the same value of x. The output values of g (x) are one-quarter the output values of f (x) for the same value of x. The output values of g (x) are the square root of the output values of f (x) for the same value of x. The output values of g (x) are the square of the output values of f (x) for the same value of x.

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Marilyn Burch · Answer 1

F (x) = 16ˣ and g (x) = 16⁽ˣ/₂⁾

Since 16 = 2⁴, then we can write:

f (x) = 2⁽⁴ˣ⁾ and g (x) = 2⁽⁴ˣ/₂⁾ = 2²ˣ

for x = 1 f (x) = 2⁴ = 16

for x = 1 g (x) = 2² = 4

(√16 = 4)

for x = 2 f (x) = 2⁸ = 256

for x = 2 g (x) = 2⁴ = 16

(√256) = 16

for x = 3 f (x) = 2¹² = 4096

for x = 1 g (x) = 2⁶ = 64

(√4096 = 64)

We notice that:

The output values of g (x) are the square root of the output values of f (x) for the same value of x.