Question

Find f(x) and g(x) so that the function can be described as y = f(g(x)). (5 points) y = eight divided by square root of quantity two x plus four.

Answer 1

• f(x) = 8/√x
• g(x) = 2x+4

Explanation:

For this sort of problem, there can be an infinite number of answers.

It can be convenient to choose one of the simpler answers by looking at the operations that are performed on the variable. Here, you have ...

• 2 multiplies it
• 4 is added to the product
• the square root is taken
• 8 is divided by that root

You can work from the bottom up and define the outer function (f(x)) to be any of these operations. In our answer above, we have elected to include the "square root" and the "8 divided by that root" in our definition of f.

Then our function g takes care of the other operations.