Answer:
33 1/3 please tank this
Step-by-step explanation:
Answer:
The domain of the function f(x) is:
![\mathrm{Domain\:of\:}\:5\left|x\right|\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:](https://tex.z-dn.net/?f=%5Cmathrm%7BDomain%5C%3Aof%5C%3A%7D%5C%3A5%5Cleft%7Cx%5Cright%7C%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)
The range of the function f(x) is:
![\mathrm{Range\:of\:}5\left|x\right|:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\ge \:0\:\\ \:\mathrm{Interval\:Notation:}&\:[0,\:\infty \:)\end{bmatrix}](https://tex.z-dn.net/?f=%5Cmathrm%7BRange%5C%3Aof%5C%3A%7D5%5Cleft%7Cx%5Cright%7C%3A%5Cquad%20%5Cbegin%7Bbmatrix%7D%5Cmathrm%7BSolution%3A%7D%5C%3A%26%5C%3Af%5Cleft%28x%5Cright%29%5Cge%20%5C%3A0%5C%3A%5C%5C%20%5C%3A%5Cmathrm%7BInterval%5C%3ANotation%3A%7D%26%5C%3A%5B0%2C%5C%3A%5Cinfty%20%5C%3A%29%5Cend%7Bbmatrix%7D)
Step-by-step explanation:
Given the function
![f\left(x\right)=5\left|x\right|](https://tex.z-dn.net/?f=f%5Cleft%28x%5Cright%29%3D5%5Cleft%7Cx%5Cright%7C)
Determining the domain:
We know that the domain of the function is the set of input or arguments for which the function is real and defined.
In other words,
- Domain refers to all the possible sets of input values on the x-axis.
It is clear that the function has undefined points nor domain constraints.
Thus, the domain of the function f(x) is:
![\mathrm{Domain\:of\:}\:5\left|x\right|\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:](https://tex.z-dn.net/?f=%5Cmathrm%7BDomain%5C%3Aof%5C%3A%7D%5C%3A5%5Cleft%7Cx%5Cright%7C%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)
Determining the range:
We also know that range is the set of values of the dependent variable for which a function is defined.
In other words,
- Range refers to all the possible sets of output values on the y-axis.
We know that the range of an Absolute function is of the form
![c|ax+b|+k\:\mathrm{is}\:\:f\left(x\right)\ge \:k](https://tex.z-dn.net/?f=c%7Cax%2Bb%7C%2Bk%5C%3A%5Cmathrm%7Bis%7D%5C%3A%5C%3Af%5Cleft%28x%5Cright%29%5Cge%20%5C%3Ak)
![k=0](https://tex.z-dn.net/?f=k%3D0)
so
Thus, the range of the function f(x) is:
![\mathrm{Range\:of\:}5\left|x\right|:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\ge \:0\:\\ \:\mathrm{Interval\:Notation:}&\:[0,\:\infty \:)\end{bmatrix}](https://tex.z-dn.net/?f=%5Cmathrm%7BRange%5C%3Aof%5C%3A%7D5%5Cleft%7Cx%5Cright%7C%3A%5Cquad%20%5Cbegin%7Bbmatrix%7D%5Cmathrm%7BSolution%3A%7D%5C%3A%26%5C%3Af%5Cleft%28x%5Cright%29%5Cge%20%5C%3A0%5C%3A%5C%5C%20%5C%3A%5Cmathrm%7BInterval%5C%3ANotation%3A%7D%26%5C%3A%5B0%2C%5C%3A%5Cinfty%20%5C%3A%29%5Cend%7Bbmatrix%7D)
Answer:
ur mom XD :/
Step-by-step explanation:
Answer:
Explanation to answers are shown in the attachment
Step-by-step explanation:
This is a long solution but the detailed step by step and appropriate mathematical manipulation has been done as shown in the attachment.