Answer:
(2, - 9 )
Step-by-step explanation:
Since 2 is the output when - 9 is input to f(x)
Then reversing the procedure, that is the inverse gives an output of - 9 for an input of 2.
(- 9, 2) is a point on the graph of f(x), then
(2, - 9) is a point on the graph o the inverse function
(x)
Step-by-step explanation:
![{2.71 \times 10}^{ - 3}](https://tex.z-dn.net/?f=%20%7B2.71%20%5Ctimes%2010%7D%5E%7B%20-%203%7D%20)
This can be rewritten as
![2.71 \times \frac{1}{10^{3} }](https://tex.z-dn.net/?f=2.71%20%5Ctimes%20%20%5Cfrac%7B1%7D%7B10%5E%7B3%7D%20%7D%20)
If we will solve this way,
![\frac{2.71}{1000} = 0.00271](https://tex.z-dn.net/?f=%5Cfrac%7B2.71%7D%7B1000%7D%20%20%3D%200.00271)
But since the denominator is just in terms of 1, we can just simply get the (-3). Note that we have to take the negative into consideration.
From the original position of the decimal point, move the decimal point 3 times TO THE LEFT. Therefore, from 2.71 we move the decimal point 3 times to the left, 0.00271.
If the exponent has a positive value, move TO THE RIGHT.
For example,
![2.71 \times {10}^{3} = 2.71 \times 1000 \\ = 2710](https://tex.z-dn.net/?f=2.71%20%5Ctimes%20%20%7B10%7D%5E%7B3%7D%20%20%3D%202.71%20%5Ctimes%201000%20%5C%5C%20%20%3D%202710)
Note that the exponent has a positive value. Therefore, we have to move the decimal point 3 times TO THE RIGHT. Producing 2710 as the answer.
Answer:
x=[15:-5:-25]'
Step-by-step explanation:
In order to create a vector you need to use this command:
x = [j:i:k]'
This creates a regularly-spaced vector x using i as the increment between elements. j is the initial value and k is the final value. Besides you need to add the character ' at the end in order to convert the arrow vector in a column vector
Answer: f(3)
Step-by-step explanation:
First find the formula for the rate of change by taking the derivative of 2^x. Let f(x) equal some hypothetical y-value, then take the natural log of both sides.
![y=2^x\\\ln(y)=x \ln(2)](https://tex.z-dn.net/?f=y%3D2%5Ex%5C%5C%5Cln%28y%29%3Dx%20%5Cln%282%29)
Implicitly differentiate the left side and take the derivative of the right side
![\frac{y'}{y} =\ln(2)](https://tex.z-dn.net/?f=%5Cfrac%7By%27%7D%7By%7D%20%3D%5Cln%282%29)
Multiply both sides by 'y' which was defined as 2^x
![y'=\ln(2)*2^x](https://tex.z-dn.net/?f=y%27%3D%5Cln%282%29%2A2%5Ex)
Plug in x = 2 and x = 3 to see which slope is larger
![y'=\ln(2)*2^2=4\ln(2)\\y'=\ln(2)*2^3=8\ln(2)](https://tex.z-dn.net/?f=y%27%3D%5Cln%282%29%2A2%5E2%3D4%5Cln%282%29%5C%5Cy%27%3D%5Cln%282%29%2A2%5E3%3D8%5Cln%282%29)
Answer:
<h2>(g-f)(10) = - 71</h2>
Step-by-step explanation:
f(x) = x² - 1
g(x) = 2x + 8
To find (g-f)(10) first find ( g - f)(x)
To find ( g - f)(x) subtract f(x) from g(x)
That's
( g - f)(x) = 2x + 8 - ( x² - 1)
Remove the bracket
( g - f)(x) = 2x + 8 - x² + 1
Simplify
( g - f)(x) = - x² + 2x + 9
To find (g-f)(10) substitute the value in the bracket that's 10 into ( g - f)(x)
That is
(g-f)(10) = -(10)² + 2(10) + 9
= - 100 + 20 + 9
= - 100 + 29
= - 71
Hope this helps you