a It's two possible orders for the functions. Try them both!
B
b Put the functions equal to -5. By solving the equations for x, what are the results?
A
a First h(x) and then g(x).
B
b Input x=6 in g(x), then this result goes into h(x).
Practice makes perfect
a Angelica has two options.
Input 6 into g(x) and then input its result into h(x).
Input 6 into h(x) and then input its result into g(x).We cannot be sure which one is correct before we've tried. Let's try the second option, to calculate h(6) first.
The output of the function is 5. This is exactly what Angelica wanted. Therefore, this is the correct order of the functions: first h(x) and then g(x).
b
We want to find an input x that will give an output of -5 after passing through two functions consecutively.
input x→function#1→function #2→ output -5To find x, we can think backwards. What input makes the second function equal to -5? We have two possibilities here. Either g(x) or h(x) is the second function.
g(x)=-5 or h(x)=-5
Since we do not know the order of the functions, let's consider what would happen if g(x) was the second function.
sqrt(x-5)=-5
The result of a square root can only be a positive number when working with real numbers. Therefore, the result of g(x) cannot be -5. Now let's consider what would happen if h(x) is second.
An input of x=1 gives us that h(x)=-5. Now, this value should be used as the output of the function g(x). Once again, this will form an equation that can be solved for x.
