Westonci.ca makes finding answers easy, with a community of experts ready to provide you with the information you seek. Experience the ease of finding accurate answers to your questions from a knowledgeable community of professionals. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.
Sagot :
Answer
The inverse function is
[tex]g^{-1}(x)=\frac{5x}{4}+\frac{25}{4}[/tex]The domain of this inverse function is all real numbers.
Explanation
The question asks us to find the invers of the given function and give any restrictions of the domain if that exists.
The function is
g(x) = -5 + (4x/5)
To obtain the inverse of a function, the right approach is to write g(x) as y, then make x the subject of formula.
[tex]\begin{gathered} y=-5+\frac{4x}{5} \\ \text{Multiply through by 5} \\ 5y=-25+4x \\ \text{Rewrite the equation} \\ -25+4x=5y \\ 4x=5y+25 \\ \text{Divide through by 4} \\ \frac{4x}{4}=\frac{5y}{4}+\frac{25}{4} \\ x=\frac{5y+25}{4} \end{gathered}[/tex]We can then write this properly in terms of the inverse function
[tex]g^{-1}(x)=\frac{5x}{4}+\frac{25}{4}[/tex]The domain of a function refers to the values of the independent variable (x), where the dependent variable [y or f(x)] or the function has a corresponding real value. The domain is simply the values of x for which the output also exists.
The domain of this inverse function is all real numbers because there would be a real number answer for every real number value of x.
Hope this Helps!!!
We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.
