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3 years ago

If g(x) is the inverse of f(x), what is the value of f(g(2))?

Mathematics

2 answers:

Elan Coil [88]3 years ago

8 0

Answer:

Step-by-step explanation:

So to figure this out we just need to flip the values of x and y in the table and then redefine that as the function g(x), because an inverse is essentially the reverse!

So if we flipped x and y's for f(x). We would see that our output or y of g(x) is -3 when x = 2, or in other words g(2) = -3. This means that we are now going to solve for when f(-3). So now lets look at the table and find the value at x = -3 for f(x). This value is 2, so the value of f(g(2)) = 2.

*In the future*

When you have a composite function of two inverses they essentially cancel out and would leave whatever the value of x is. So if we know f(x) and g(x) were inverses the value of f(g(2)) would just be 2.

For example:

ln(x) and e^x are inverses so if I had a composition like this:

$e^{ln(2)}$

The answer to this would be 2 because these inverse functions "'cancel" out

$e^{ln2} = 2$

Artyom0805 [142]3 years ago

6 0

Answer:

The answer is C on edge 2020

Step-by-step explanation:

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Hugo is designing a frame as shown at the right. The frame has a width of x inches all the way around. Write. an expression that

Cloud [144]

The expression which shows the total area of the picture and frame is $x^{2} +72x$ +320.

Given that the width of the frame is x ,length horizontally be 20 inches and vertically be 16 inches.

We are required to find the expression which shows the total area of the picture and frame.

Expression is basically a combination of numbers, symbols, coefficients, determinants, indeterminants,etc. and are mostly not found in equal to form.

Since we are given that the width of the frame be x, So,the are of only frame will be :

Area of frame=20*x*2+16*x*2+x*x

=40x+32x+ $x^{2}$

= $x^{2}$ +72x

Area of picture=20*16=320 $inches^{2}$

The expression which shows the total area of the picture and frame is $x^{2} +72x$ +320.

Hence the expression which shows the total area of the picture and frame is $x^{2} +72x$ +320.

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2 years ago

Researchers at a lake have determined that the percentage of fish in the lake that are intolerant to pollution can be estimated

dusya [7]

Answer:

a. 23.02 %

b. 49%

c. W

Step-by-step explanation:

Solution:-

- A multi-variable function for the percentage of fish in the lake that are intolerant to the pollution is given as:

$P ( W , R , A ) = 49 - 1.61W - 1.41R - 1.38A$

Where,

W: percentage of wetland

R: percentage of residential area

A: percentage of agriculture

- We are to evaluate the percentage of fish intolerant to pollution in the case where W = 3 , R = 15 , A = 0. We will plug in the values in the modeled function P ( W , R , A ) as follows:

$P ( 3 , 15 , 0 ) = 49 - 1.61*3 - 1.41*15 -1.38*0\\\\P ( 3 , 15 , 0 ) = 23.02\\$

- To determine the maximum percentage of fish that will be intolerant to pollution we will employ the use of critical points. The critical point that is defined by the linear relationship between P and all other parameters ( W, R , A ). The maximum value occurs when W = R = A = 0.

$P ( 0 , 0 , 0 ) = 49 - 1.61*0 -1.41*0 - 1.38*0 = 49$

- Hence, the maximum value of the function is 49%.

- The linear relationship between each induvidual parameter ( R, W , A ) and the function ( P ) is proportional in influence. The extent of influence can be quantized by the constant multiplied by each parameter.

- We see that that ( 1.61*W ) > ( 1.41R ) > ( 1.38A ). The greatest influence is by parameter ( W ) i.e the influence of percentage of wetlands .

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3 years ago

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juin [17]

Answer:

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