Answer:
A
Step-by-step explanation:
![(f-g)(x)=f(x)-g(x)\\=(x-2)-(x^2+3x-4)\\=x-2-x^2-3x+4\\=-x^2-4x+2\\](https://tex.z-dn.net/?f=%28f-g%29%28x%29%3Df%28x%29-g%28x%29%5C%5C%3D%28x-2%29-%28x%5E2%2B3x-4%29%5C%5C%3Dx-2-x%5E2-3x%2B4%5C%5C%3D-x%5E2-4x%2B2%5C%5C)
Therefore, answer is A.
To reflect the function across the x axis, we must multiply the whole thing by -1
f(kx) is the answer to make the thing negative
so you should result with
f(x)=-x^2
basically the answer is D
That the answer ur welcome
Answer:
2.66 (rounded to the nearest hundredth)
Using integration, it is found that the area of the shaded region is of
units squared.
<h3>How is the area of a shaded region found?</h3>
- The area of shaded region, between two curves
and
, considering
, between x = a and x = b, is given by the following integral:
![A = \int_a^b f(x) - g(x) dx](https://tex.z-dn.net/?f=A%20%3D%20%5Cint_a%5Eb%20f%28x%29%20-%20g%28x%29%20dx)
In this problem, the curves are:
![f(x) = \sqrt[3]{x} = x^{\frac{1}{3}}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Csqrt%5B3%5D%7Bx%7D%20%3D%20x%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D)
![g(x) = \frac{1}{x}](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Cfrac%7B1%7D%7Bx%7D)
The limits of integration are:
.
Hence:
![A = \int_1^{27} \left(x^{\frac{1}{3}} - \frac{1}{x}\right) dx](https://tex.z-dn.net/?f=A%20%3D%20%5Cint_1%5E%7B27%7D%20%5Cleft%28x%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%20-%20%5Cfrac%7B1%7D%7Bx%7D%5Cright%29%20dx)
Applying the power properties of integration:
![A = 3x^{\frac{4}{3}} - \ln{x}|_{x = 1}^{x = 27}](https://tex.z-dn.net/?f=A%20%3D%203x%5E%7B%5Cfrac%7B4%7D%7B3%7D%7D%20-%20%5Cln%7Bx%7D%7C_%7Bx%20%3D%201%7D%5E%7Bx%20%3D%2027%7D)
Finally, applying the Fundamental Theorem of Calculus:
![A = 3(27)^{\frac{4}{3}} - \ln{27} - 3(1)^{\frac{4}{3}} + \ln{1}](https://tex.z-dn.net/?f=A%20%3D%203%2827%29%5E%7B%5Cfrac%7B4%7D%7B3%7D%7D%20-%20%5Cln%7B27%7D%20-%203%281%29%5E%7B%5Cfrac%7B4%7D%7B3%7D%7D%20%2B%20%5Cln%7B1%7D)
![A = 240 - \ln{27}](https://tex.z-dn.net/?f=A%20%3D%20240%20-%20%5Cln%7B27%7D)
The area of the shaded region is of
units squared.
To learn more about integration, you can take a look at brainly.com/question/20733870