Answer:32
Step-by-step explanation:96-64=32 half of 64 is 32 also equal to 50%
Answer:
the are is 14
brainliest??
Step-by-step explanation:
The answer and the working out is in the attached sheet! :)
Answer:
Please check the answer below in detail.
Step-by-step explanation:
The correct form of the function is
![f(x)=\frac{1}{3}(81)^{\frac{3x}{4}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7B1%7D%7B3%7D%2881%29%5E%7B%5Cfrac%7B3x%7D%7B4%7D)
Lets simplify
![f(x)=\frac{1}{3}\cdot \:81^{\frac{3x}{4}}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7B1%7D%7B3%7D%5Ccdot%20%5C%3A81%5E%7B%5Cfrac%7B3x%7D%7B4%7D%7D)
![f(x)=\frac{1}{3}\cdot \:(3^{4}) ^{\frac{3x}{4}}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7B1%7D%7B3%7D%5Ccdot%20%5C%3A%283%5E%7B4%7D%29%20%5E%7B%5Cfrac%7B3x%7D%7B4%7D%7D)
![\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc}](https://tex.z-dn.net/?f=%5Cmathrm%7BApply%5C%3Aexponent%5C%3Arule%7D%3A%5Cquad%20%5Cleft%28a%5Eb%5Cright%29%5Ec%3Da%5E%7Bbc%7D)
![\left(3^4\right)^{\frac{3x}{4}}=3^{4\cdot \frac{3x}{4}}=3^{3x}](https://tex.z-dn.net/?f=%5Cleft%283%5E4%5Cright%29%5E%7B%5Cfrac%7B3x%7D%7B4%7D%7D%3D3%5E%7B4%5Ccdot%20%5Cfrac%7B3x%7D%7B4%7D%7D%3D3%5E%7B3x%7D)
So, the function f(x) becomes
![f(x)=\frac{1}{3}\cdot \:3^{3x}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7B1%7D%7B3%7D%5Ccdot%20%5C%3A3%5E%7B3x%7D)
Use the exponent rule ![\frac{a^m}{a^n}=a^{m-n}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%5Em%7D%7Ba%5En%7D%3Da%5E%7Bm-n%7D)
The simplified form of the given function would be:
![f(x)=3^{3x-1}](https://tex.z-dn.net/?f=f%28x%29%3D3%5E%7B3x-1%7D)
As domain is considered to be the set of all possible input values of x for which the function is defined.
So,
![\mathrm{Domain\:of\:}\:\frac{1}{3}\cdot \:27^x\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:](https://tex.z-dn.net/?f=%5Cmathrm%7BDomain%5C%3Aof%5C%3A%7D%5C%3A%5Cfrac%7B1%7D%7B3%7D%5Ccdot%20%5C%3A27%5Ex%5C%3A%3A%5Cquad%20%5Cbegin%7Bbmatrix%7D%5Cmathrm%7BSolution%3A%7D%5C%3A%26%5C%3A-%5Cinfty%20%5C%3A%3Cx%3C%5Cinfty%20%5C%5C%20%5C%3A%5Cmathrm%7BInterval%5C%3ANotation%3A%7D%26%5C%3A%5Cleft%28-%5Cinfty%20%5C%3A%2C%5C%3A%5Cinfty%20%5C%3A%5Cright%29%5Cend%7Bbmatrix%7D)
As range is the set of dependent variable for which the function is defined.
As
![\mathrm{The\:range\:of\:an\:exponential\:function\:of\:the\:form}\:c\cdot \:n^{ax+b}+k\:\mathrm{is}\:\:f\left(x\right)>k](https://tex.z-dn.net/?f=%5Cmathrm%7BThe%5C%3Arange%5C%3Aof%5C%3Aan%5C%3Aexponential%5C%3Afunction%5C%3Aof%5C%3Athe%5C%3Aform%7D%5C%3Ac%5Ccdot%20%5C%3An%5E%7Bax%2Bb%7D%2Bk%5C%3A%5Cmathrm%7Bis%7D%5C%3A%5C%3Af%5Cleft%28x%5Cright%29%3Ek)
![k=0](https://tex.z-dn.net/?f=k%3D0)
![f\left(x\right)>0](https://tex.z-dn.net/?f=f%5Cleft%28x%5Cright%29%3E0)
Therefore,
![\mathrm{Range\:of\:}\frac{1}{3}\cdot \:27^x:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)>0\:\\ \:\mathrm{Interval\:Notation:}&\:\left(0,\:\infty \:\right)\end{bmatrix}](https://tex.z-dn.net/?f=%5Cmathrm%7BRange%5C%3Aof%5C%3A%7D%5Cfrac%7B1%7D%7B3%7D%5Ccdot%20%5C%3A27%5Ex%3A%5Cquad%20%5Cbegin%7Bbmatrix%7D%5Cmathrm%7BSolution%3A%7D%5C%3A%26%5C%3Af%5Cleft%28x%5Cright%29%3E0%5C%3A%5C%5C%20%5C%3A%5Cmathrm%7BInterval%5C%3ANotation%3A%7D%26%5C%3A%5Cleft%280%2C%5C%3A%5Cinfty%20%5C%3A%5Cright%29%5Cend%7Bbmatrix%7D)
Graph is also attached from where you can observe all the key aspects which have been discussed above.
Keywords: domain, range, function, graph
Learn more about domain, range, function and graph from brainly.com/question/13882944
#learnwithBrainly