Finding the inverse function of
, it is best described by graph B.
<h3>How to find the inverse of a function?</h3>
Supposing we have a function y = f(x), to find the inverse, we exchange x and y, and isolate y.
In this problem, the function is:
![f(x) = 5\sqrt{x + 3} - 2](https://tex.z-dn.net/?f=f%28x%29%20%3D%205%5Csqrt%7Bx%20%2B%203%7D%20-%202)
![y = 5\sqrt{x + 3} - 2](https://tex.z-dn.net/?f=y%20%3D%205%5Csqrt%7Bx%20%2B%203%7D%20-%202)
Exchanging x and y:
![x = 5\sqrt{y + 3} - 2](https://tex.z-dn.net/?f=x%20%3D%205%5Csqrt%7By%20%2B%203%7D%20-%202)
Working through the function to isolate y:
![5\sqrt{y + 3} = x + 2](https://tex.z-dn.net/?f=5%5Csqrt%7By%20%2B%203%7D%20%3D%20x%20%2B%202)
![\sqrt{y + 3} = \frac{x + 2}{5}](https://tex.z-dn.net/?f=%5Csqrt%7By%20%2B%203%7D%20%3D%20%5Cfrac%7Bx%20%2B%202%7D%7B5%7D)
![(\sqrt{y + 3})^2 = \left(\frac{x + 2}{5}\right)^2](https://tex.z-dn.net/?f=%28%5Csqrt%7By%20%2B%203%7D%29%5E2%20%3D%20%5Cleft%28%5Cfrac%7Bx%20%2B%202%7D%7B5%7D%5Cright%29%5E2)
![y + 3 = \frac{(x + 2)^2}{25}](https://tex.z-dn.net/?f=y%20%2B%203%20%3D%20%5Cfrac%7B%28x%20%2B%202%29%5E2%7D%7B25%7D)
![y = \frac{(x + 2)^2}{25} - 3](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B%28x%20%2B%202%29%5E2%7D%7B25%7D%20-%203)
![f^{-1}(x) = \frac{(x + 2)^2}{25} - 3](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%20%3D%20%5Cfrac%7B%28x%20%2B%202%29%5E2%7D%7B25%7D%20-%203)
Which is best represented by graph B.
More can be learned about inverse functions at brainly.com/question/27830327
#SPJ1
Step-by-step explanation:
Here n = 8 (even number)
![\therefore \: \frac{n}{2} = \frac{8}{2} = 4 \\ \\\&\:\: \frac{n}{2} + 1 = 4 + 1 = 5 \\ \\ hence \: \\ median = \frac{ {4}^{th} term + {5}^{th} term}{2} \\ \\ \therefore \: 49 = \frac{x - 1 + x + 1}{2} \\ \\ \therefore \: 49 = \frac{2x}{2} \\ \\ \therefore \: 49 = x \\ \\ \huge \purple { \boxed{\therefore \: x = 49}}](https://tex.z-dn.net/?f=%20%5Ctherefore%20%5C%3A%20%20%5Cfrac%7Bn%7D%7B2%7D%20%20%3D%20%20%5Cfrac%7B8%7D%7B2%7D%20%20%3D%204%20%5C%5C%20%20%5C%5C%5C%26%5C%3A%5C%3A%20%20%20%5Cfrac%7Bn%7D%7B2%7D%20%20%2B%201%20%3D%204%20%2B%201%20%3D%205%20%5C%5C%20%20%5C%5C%20hence%20%5C%3A%20%20%5C%5C%20median%20%3D%20%5Cfrac%7B%20%7B4%7D%5E%7Bth%7D%20term%20%2B%20%20%7B5%7D%5E%7Bth%7D%20term%7D%7B2%7D%20%20%5C%5C%20%20%5C%5C%20%20%5Ctherefore%20%5C%3A%20%2049%20%3D%20%20%5Cfrac%7Bx%20-%201%20%2B%20x%20%2B%201%7D%7B2%7D%20%20%5C%5C%20%20%5C%5C%20%20%5Ctherefore%20%5C%3A%20%2049%20%3D%20%20%5Cfrac%7B2x%7D%7B2%7D%20%5C%5C%20%20%5C%5C%20%20%5Ctherefore%20%5C%3A%20%2049%20%3D%20x%20%5C%5C%20%20%5C%5C%20%20%5Chuge%20%5Cpurple%20%7B%20%5Cboxed%7B%5Ctherefore%20%5C%3A%20x%20%3D%2049%7D%7D)
Answer:
yes
Step-by-step explanation:
Answer:
1) ![f'(t)=4t,\ g'(t)=3t^2+4](https://tex.z-dn.net/?f=f%27%28t%29%3D4t%2C%5C%20g%27%28t%29%3D3t%5E2%2B4)
2) ![p(t) =2t^5+8t^3](https://tex.z-dn.net/?f=p%28t%29%20%3D2t%5E5%2B8t%5E3)
![p'(t)=10t^4+24t^2](https://tex.z-dn.net/?f=p%27%28t%29%3D10t%5E4%2B24t%5E2)
3) False
4)![q(t) =\dfrac{1}{2}t+2t^{-1}](https://tex.z-dn.net/?f=q%28t%29%20%3D%5Cdfrac%7B1%7D%7B2%7Dt%2B2t%5E%7B-1%7D)
![q'(t)=\dfrac{1}{2}-\dfrac{2}{t^2}](https://tex.z-dn.net/?f=q%27%28t%29%3D%5Cdfrac%7B1%7D%7B2%7D-%5Cdfrac%7B2%7D%7Bt%5E2%7D)
5) False
Step-by-step explanation:
Given that:
and ![g(t) = t^3 + 4t](https://tex.z-dn.net/?f=g%28t%29%20%3D%20t%5E3%20%2B%204t)
Formula:
![1. \dfrac{d}{dx}x^n=nx^{n-1}](https://tex.z-dn.net/?f=1.%20%5Cdfrac%7Bd%7D%7Bdx%7Dx%5En%3Dnx%5E%7Bn-1%7D)
![2. \dfrac{d}{dx}C.f(x)=C.f'(x)\ \{\text{C is a constant}\}](https://tex.z-dn.net/?f=2.%20%5Cdfrac%7Bd%7D%7Bdx%7DC.f%28x%29%3DC.f%27%28x%29%5C%20%5C%7B%5Ctext%7BC%20is%20a%20constant%7D%5C%7D)
1) Using above formula:
![f'(t)=2\times 2 t^{2-1}=4t](https://tex.z-dn.net/?f=f%27%28t%29%3D2%5Ctimes%202%20t%5E%7B2-1%7D%3D4t)
![g'(t)=3t^{3-1}+4\times 1 t^{1-1}=3t^2+4](https://tex.z-dn.net/?f=g%27%28t%29%3D3t%5E%7B3-1%7D%2B4%5Ctimes%201%20t%5E%7B1-1%7D%3D3t%5E2%2B4)
2) ![p(t) =2t^2(t^3+4t)](https://tex.z-dn.net/?f=p%28t%29%20%3D2t%5E2%28t%5E3%2B4t%29)
Rewriting the formula by distributing the
term:
![p(t) =2t^2.t^3+2t^2.4t=2t^5+8t^3](https://tex.z-dn.net/?f=p%28t%29%20%3D2t%5E2.t%5E3%2B2t%5E2.4t%3D2t%5E5%2B8t%5E3)
![p'(t) = 10t^4+24t^2](https://tex.z-dn.net/?f=p%27%28t%29%20%3D%2010t%5E4%2B24t%5E2)
3) By using answers of part (1):
![f'(t).g'(t)=12t^3+16t](https://tex.z-dn.net/?f=f%27%28t%29.g%27%28t%29%3D12t%5E3%2B16t)
![p'(t) = 10t^4+24t^2](https://tex.z-dn.net/?f=p%27%28t%29%20%3D%2010t%5E4%2B24t%5E2)
Therefore it is <em>False </em> that ![p'(t) = f'(t).g'(t)](https://tex.z-dn.net/?f=p%27%28t%29%20%3D%20f%27%28t%29.g%27%28t%29)
4) ![q(t)=\dfrac{t^3+4t}{2t^2}](https://tex.z-dn.net/?f=q%28t%29%3D%5Cdfrac%7Bt%5E3%2B4t%7D%7B2t%5E2%7D)
Writing by distributing:
![q(t)=\dfrac{t^3}{2t^2}+\dfrac{4t}{2t^2}\\\Rightarrow q(t) =\dfrac{t}{2}+\dfrac{2}{t}\\\Rightarrow q(t) =\dfrac{1}{2}t+2t^{-1}](https://tex.z-dn.net/?f=q%28t%29%3D%5Cdfrac%7Bt%5E3%7D%7B2t%5E2%7D%2B%5Cdfrac%7B4t%7D%7B2t%5E2%7D%5C%5C%5CRightarrow%20q%28t%29%20%3D%5Cdfrac%7Bt%7D%7B2%7D%2B%5Cdfrac%7B2%7D%7Bt%7D%5C%5C%5CRightarrow%20q%28t%29%20%3D%5Cdfrac%7B1%7D%7B2%7Dt%2B2t%5E%7B-1%7D)
Using the formula:
![q'(t)=\dfrac{1}{2}t^{1-1}+2\dfrac{-1}{t^2}\\\Rightarrow q'(t)=\dfrac{1}{2}-\dfrac{2}{t^2}](https://tex.z-dn.net/?f=q%27%28t%29%3D%5Cdfrac%7B1%7D%7B2%7Dt%5E%7B1-1%7D%2B2%5Cdfrac%7B-1%7D%7Bt%5E2%7D%5C%5C%5CRightarrow%20q%27%28t%29%3D%5Cdfrac%7B1%7D%7B2%7D-%5Cdfrac%7B2%7D%7Bt%5E2%7D)
(5)By using answers in part (1):
![\dfrac{g'(t)}{f'(t)}=\dfrac{3t^2+4}{4t}=\dfrac{3}{4}t+\dfrac{1}t](https://tex.z-dn.net/?f=%5Cdfrac%7Bg%27%28t%29%7D%7Bf%27%28t%29%7D%3D%5Cdfrac%7B3t%5E2%2B4%7D%7B4t%7D%3D%5Cdfrac%7B3%7D%7B4%7Dt%2B%5Cdfrac%7B1%7Dt)
![q'(t)=\dfrac{1}{2}-\dfrac{2}{t^2}](https://tex.z-dn.net/?f=q%27%28t%29%3D%5Cdfrac%7B1%7D%7B2%7D-%5Cdfrac%7B2%7D%7Bt%5E2%7D)
Therefore, it is <em>False </em>that:
![q'(t)=\dfrac{g'(t)}{f'(t)}](https://tex.z-dn.net/?f=q%27%28t%29%3D%5Cdfrac%7Bg%27%28t%29%7D%7Bf%27%28t%29%7D)
Answer:
50
Step-by-step explanation:
22 is 44% of 50. It's 50 because it's techincally half if you look at it. I don't know how to really explain that well. But the answer is 50, trust me.