A square root cannot give a negative value. What does this mean for the order in which you have to use the functions?
A
a
y=x^2-6 → y=sqrt(x-5)
B
b
Yes, it is possible. See solution.
a
Let's start by labeling the given functions.
Function A:& y=sqrt(x-5)
Function B:& y=x^2-6
By examining the functions, it might not be clear which one we should start with. We will begin by substituting x=6 into one of the functions and evaluating. Then, we will make the output from that function the input of the second function.
Since our final output is y=5, we can conclude that we must begin with B.
b
Let's remember our labels.
Function A:& y=sqrt(x-5)
Function B:& y=x^2-6To begin, we recognize that a square root can never give a negative value. Therefore, we know that we have to start with A. However, to do this exercise, we will actually work backwards. First, we will find which input of B gives the desired output of y=-5.
We have two inputs that would make B equal - 5. However, as previously explained, a square root can only produce a positive value. Therefore, the only valid output from A is x=1. With this information, we can solve for which input of A will produce this output.
