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Sophie [7]
3 years ago
11

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.
Mathematics
1 answer:
zubka84 [21]3 years ago
6 0

Answer:

  • f(x) = 8/√x
  • g(x) = 2x+4

Step-by-step 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.

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Answer:

5 terms

to the fourth degree

leading coeff of 1

3 turning points

end behavior (when x -> inf, y -> inf. When x -> - inf, y -> -inf)

x intercepts are (0,-4) (0,-2) (0,1) (0,3)

Relative min: (-3.193, -25) (2.193, 25)

Relative max: (-0.5, 27.563)

Step-by-step explanation:

The terms can be counted, seperated by the + and - in the equation given.

The highest exponent is your degree.

The number before the highest term is your leading coeff, if there is no number it is 1.

The turning points are where the graph goes from falling to increasing or vice versa.

End behaviour you have to look at what why does when x goes to -inf and inf.

X int are the points at which the graph crosses the x-axis.

The relative min and max are findable if you plug in the graph on desmos or a graphing calculator.

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Step-by-step explanation:

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