<em><u>Method One</u></em>
f(g(x)) = x
<em><u>Method Two</u></em>
g(f(x)) = x
So let's pick a pair of functions and try this out.
f(x) = x^2 + 1
g(x) =sqrt(x - 1)
<em><u>Using Method 1</u></em>
f(g(x)) = (g(x)^2 + 1 You put a g(x) wherever you see an x in f(x)
f(g(x)) = [sqrt(x - 1)}^2 + 1 Substitute the right side of g(x) on the right side of f(x)
f(g(x)) = x - 1 + 1 Expand and cancel
f(g(x) = x
<em><u>Using Method 2</u></em>
g(f(x)) = sqrt(f(x) - 1) Put an f(x) wherever you see an x in g(x)
g(f(x)) = sqrt(x^2 + 1 - 1) Substitute the value of f(x) in the g(x) equation
g(f(x)) = sqrt(x^2) The 1s cancel. Take the square root of x^2
g(f(x)) = x You get x which is what you need to get.
So these two functions are the inverses of each other. Both methods confirm the results. A graph may help you to understand.
Notice how the red line (f(x) = x^2 + 1) is reflected across the green line to become the blue line (g(x) = sqrt(x - 1) ) That is another way to tell that 2 equations are inverses.
Note further that I have take the equations so that x in all three cases is ≥ 0
ok I will help u tomorrow I am busy today
In 10 minutes Joey eat 52 hot dogs
Step-by-step explanation:
In one minute Joey can eat 5.2 hot dogs
In 10 minutes how many hot dogs should Joey eat?
Solving:
In one minute Joey can eat hot dogs = 5.2
In 10 minutes Joey can eat hot dogs = 5.2*10
In 10 minutes Joey can eat hot dogs = 52
So, in 10 minutes Joey eat 52 hot dogs
Keywords: Word Problems
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Answer:
24 degrees
Step-by-step explanation:
A Ferris wheel is in the shape of a circle. Having 15 seat buckets means that the circle will be divided into 15 sections. Keep in mind that we are assuming that the seat buckets are equally spaced.
We know that:
Degrees in one circle: 360 degree
Dividing in 15 sections:
So the angle of measurement between the seat buckets is 24 degrees ..