The inverse of the function f(x) is Option (A) [tex]f^{-1}(x) = \frac{3(x - 5)}{5}[/tex]
Finding the inverse of a function f(x) -
To find the inverse of any function, we follow some steps which are -
- First substitute the value of f(x) as y and represent the same equation.
- Then we find the value of x making y as the dependent variable.
- After that we just replace the variable y by x and x by inverse function and therefore find the inverse function of f(x) .
Thus following the same steps in the question,
Given [tex]f(x) = \frac{5x}{3} + 5[/tex]
⇒ [tex]y = \frac{5x}{3} + 5[/tex]
⇒ [tex]y - 5 = \frac{5x}{3}[/tex]
⇒ [tex]3(y - 5) = 5x[/tex]
∴ [tex]x = \frac{3(y - 5)}{5}[/tex]
Replacing the variables in the last step ,
∴ [tex]f^{-1}(x) = \frac{3(x - 5)}{5}[/tex] which is Option (A)
To learn more about inverse function, refer -
https://brainly.com/question/11735394
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