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stellarik [79]
2 years ago
11

The composition of a function and its inverse is always

Mathematics
2 answers:
rusak2 [61]2 years ago
7 0

Lets try this with an example.

Suppose we have a function f(x)=2x.

Calculate its inverse f^{-1}(x)=\dfrac{x}{2}.

And now just simply try to find the composition,

f(f^{-1}(x))=f\Big(\dfrac{x}{2}\Big)=2\cdot\dfrac{x}{2}=x.

The answer is the composition of a function and its inverse is always function g(x)=f(f^{-1}(x))=\boxed{x}.

Hope this helps.

dusya [7]2 years ago
4 0

Answer:               x

Step-by-step explanation:

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olasank [31]

OPTION A is the correct answer.

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2 years ago
A rectangular aquarium 3 ft. x 2 ft. 1 ft. is 2/3 full of water. In cubic feet, how much water is in the tank
tatuchka [14]

To find the volume of a rectangular prism, we must multiply the length * width * height.


In this case,


Volume = 3 ft * 2 ft * 1 ft

= 6 ft^3


Because this tank is 2/3 full with water, to find out how much water is in the tank, we must multiply 2/3 by the total volume of the tank (6 ft^3).


2/3 * 6 ft^3 = 4 ft^3


This means that there are 4 cubic feet of water in the tank.


Hope this helps!

6 0
3 years ago
Find f(x) and g(x) so that the function can be described as y = f(g(x)).<br><br> y = 4/x^2+9
dlinn [17]

I'm assuming all of (x^2+9) is in the denominator. If that assumption is correct, then,

One possible answer is f(x) = \frac{4}{x},  \ \ g(x) = x^2+9

Another possible answer is f(x) = \frac{4}{x+9}, \ \ g(x) = x^2

There are many ways to do this. The idea is that when we have f( g(x) ), we basically replace every x in f(x) with g(x)

So in the first example above, we would have

f(x) = \frac{4}{x}\\\\f( g(x) ) = \frac{4}{g(x)}\\\\f( g(x) ) = \frac{4}{x^2+9}

In that third step, g(x) was replaced with x^2+9 since g(x) = x^2+9.

Similar steps will happen with the second example as well (when g(x) = x^2)

4 0
3 years ago
The altitude a ( in feet) of a plane t minutes after lift off is given by a=3400t+600
Julli [10]

Answer:

  6 minutes

Step-by-step explanation:

'a' in the formula represents altitude in feet. You are told the altitude is 21000 feet, so put that into the formula:

   21000 = 3400t +600

You can solve this for t:

  20400 = 3400t . . . . . subtract 600 from both sides

  6 = t . . . . . . . . . . . . . . . divide both sides by 3400

The problem statement tells you that t represents minutes after lift off, so this solution means the altitude is 21000 feet 6 minutes after lift off.

The question is asking for the number of minutes after lift off that the plane reaches an altitude of 21000 feet, so this answers the question directly:

  The plane is at an altitude of 21000 feet 6 minutes after lift off.

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2 years ago
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Answer:

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Step-by-step explanation:

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