Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. (5 points)

1 answer:

8 0

F(x)=(x-8)/(x+7). g(x)=(-7x-8)/(x-1). Plug in g(x) into f(x), f(g(x))=[(-7x-8)/(x-1)-8]/[-7x-8)/(x-1)+7], which can be simplified as (-7x-8-8x+8)/(-7x-8+7x-7)=-15x/-15=x. Plug in f(x) into g(x), g(f(x))=[-7*(x-8)/(x+7)-8]/[(x-8)/(x+7)-1]=(-7x+56-8x-56)/(x-8-x-7)=-15x/-15=x, as desired.

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A new bridge structure requires triangles that are in a ratio of 1:1. If AC = 2x + 10 and EC = 4x − 18, find the distance betwee

gavmur [86]

Answer: The required distance between the top and bottom of the bridge is 76 feet.

Step-by-step explanation: Given that a new bridge structure requires triangles that are in a ratio of 1:1.

AC = 2x + 10 and EC = 4x − 18.

We are to find the distance between the top and bottom of the bridge, in feet.

Since the two triangles ACB and DCE are in the ratio 1 : 1, so their corresponding sides are also in the ratio 1 : 1.

The sides AC and EC are corresponding to each other, so we must have

$AC:EC=1:1\\\\\Rightarrow \dfrac{AC}{EC}=\dfrac{1}{1}\\\\\Rightarrow AC=EC\\\\\Rightarrow 2x+10=4x-18\\\\\Rightarrow 4x-2x=10+18\\\\\Rightarrow 2x=28\\\\\Rightarrow x=\dfrac{28}{2}\\\\\Rightarrow x=14.$