Answer:
Choice C
Step-by-step explanation:
We are given the function:
[tex]\displaystyle \large{f(x)=3x+5}[/tex]
Let [tex]\displaystyle \large{y=f(x)}[/tex] therefore:
[tex]\displaystyle \large{y=3x+5}[/tex]
To find an inverse of function, swap the position of x and y:
[tex]\displaystyle \large{x=3y+5}[/tex]
Then solve or simplify the equation in term of y:
[tex]\displaystyle \large{x-5=3y}\\\displaystyle \large{\frac{x-5}{3}=y}\\\displaystyle \large{y=\frac{1}{3}x-\frac{5}{3}}[/tex]
Therefore, the answer is choice C.
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Summary
An inverse function is a function that swaps the position of domain and range, defined as notation [tex]\displaystyle \large{f^{-1}(x)}[/tex] or [tex]\displaystyle \large{y^{-1}}[/tex] generally. When finding an inverse function, make sure to swap position of range and domain, if given the interval.
Only one-to-one functions may have an inverse — multiple-to-one can not have an inverse such as quadratic function or any even-degree polynomial functions.
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Others
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