F(g(x)) = [(-7x-8)/(x-1) - 8} / [(-7x - 8)/(x-1) + 7] =
[(-7x - 8 - 8(x-1)) / (x-1)] / [(-7x - 8 + 7(x-1)) / (x-1)] = (-15x) / (-15) = x.
g(f(x)) = [-7*(x-8)/(x+7) - 8] / [(x-8)/(x+7) - 1] =
[(-7x + 56 -8*(x+7)) / (x+7)] / [(x - 8 - (x + 7)) / (x+7)] = (-15x) / (-15) = x.
So since f(g(x)) = g(f(x)) = x we can conclude that f and g are inverses.
The function that describes the graph is an exponential function
<h3>How to determine the function type?</h3>
From the graph, we have the following highlights:
- Initially, when x increases; y seem not to increase
- Then, x and y increase at the same time
- Finally, y increase and x seem not to increase
The above is the description of an exponential function
Hence, the function that describes the graph is an exponential function
Read more about exponential function at:
brainly.com/question/11464095
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9514 1404 393
Answer:
y -10 = 1/8(x +8)
Step-by-step explanation:
The point-slope form of the equation of a line with slope m through point (h, k) is ...
y -k = m(x -h)
You have m = 1/8, and (h, k) = (-8, 10).
Putting those numbers in the form gives ...
y -10 = 1/8(x -(-8))
You can simplify the double minus sign so you have ...
y -10 = 1/8(x +8)
_____
<em>Additional comment</em>
A lot of math is about matching patterns and making substitutions. This is a good example of that.
Answer:
t as a function of height h is t = √600 - h/16
The time to reach a height of 50 feet is 5.86 minutes
Step-by-step explanation:
Function for height is h(t) = 600 - 16t²
where t = time lapsed in seconds after an object is dropped from height of 600 feet
t as a function of height h
replacing the function with variable h
h = 600 - 16t²
Solving for t
Subtracting 600 from both side
h - 600 = -16t²
Divide through by -16
600 - h/ 16 = t²
Take square root of both sides
√600 - h/16 = t
Therefore, t = √600 - h/16
Time to reach height 50 feet
t = √600 - h/16
substituting h = 50 in the equation
t = √600 - 50/16
t = √550/16
t= 34.375
t = 5.86 minutes
Probably 5, the actually answer is about 4.4347 so that’s the answer in my opinion
