Question

In what order should you stack the machines so that

Answer 1

Answer:

$g(x) = -(x - 2)^2$

$k(x) = -\frac{x}{2} - 1$

$h(x) = 2^x - 7$

$f(x) =\sqrt{x}$

Step-by-step explanation:

Given

Input = 6

Expected Output = 11

Process:

$f(x) =\sqrt{x}$

$g(x) = -(x - 2)^2$

$h(x) = 2^x - 7$

$k(x) = -\frac{x}{2} - 1$

Required

Arrange the processes to give an output of 11

To answer this question, I'll make use of trial by error methods.

After some attempts, the following is the order of the processes;

Set x = 6

Substitute 6 for x in g(x)

$g(x) = -(x - 2)^2$

$g(6) = -(6 - 2)^2$

$g(6) = -(4)^2$

$g(6) = -16$

Substitute -16 for x in k(x)

$k(-16) = -\frac{-16}{2} - 1$

$k(-16) = -(-8) - 1$

$k(-16) = 8 - 1$

$k(-16) = 7$

Substitute 7 for x in h(x)

$h(x) = 2^x - 7$

$h(7) = 2^7 - 7$

$h(7) = 128 - 7$

$h(7) = 121$

Substitute 121 for x in f(x)

$f(x) =\sqrt{x}$

$f(121) = \sqrt{121}$

$f(121) = 11$

Hence, the processes is:

$g(x) = -(x - 2)^2$

$k(x) = -\frac{x}{2} - 1$

$h(x) = 2^x - 7$

$f(x) =\sqrt{x}$