Question

Select the correct answer from each drop-down menu.

Consider functions h and k.
h(z) = 52² - 1
k(z) = √5z + 1
Forz 20. the value of h(k(z)) is
For 20. functions h and k
are not
are
the value of k(h(z)).
inverse functions.
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Answer 1

To find h(k(z)), insert k(z) into h(z): h(k(z)) = 5(√5z + 1)² - 1. The functions h(z) and k(z) are not inverse functions because h(k(z)) is not equal to z.

Step-by-step explanation:

The student is asking about the composition of two functions, h(z) and k(z), and whether they are inverse functions. The functions are given as h(z) = 5z² - 1 and k(z) = √5z + 1.

To find the value of h(k(z)), one must first apply k(z) and then apply h to the result.

To determine whether the functions are inverses, we check if h(k(z)) = z and k(h(z)) = z for all values in the domain of z ≥ 0.

To find h(k(z)), we replace z in h(z) with k(z):
h(k(z)) = h(√5z + 1)

= 5(√5z + 1)² - 1

= 5(5z + 2√5z + 1) - 1

= 25z + 10√5z + 4.
This is not equal to z, so they are not inverse functions.