Answer:
[tex]y^{-1}(x) = \frac{x-65}5\\\\f^{-1}(t)=7-2t\\\\P^{-1}(n) = 3n+3.6[/tex]
Step-by-step explanation:
To find the inverse of a function, you should first swap places between every occurrence of the independent variable and that of the dependent variable, also replacing every instance of the dependent variable with the sign of its inverse. After doing so, you may solve for the dependent variable to get the inverse of the function.
A.
[tex]y(x) = 65 + 5x \to x = 65 + 5y^{-1}(x)\\\\x = 65 + 5y^{-1}(x)\\x - 65 = 5y^{-1}(x)\\y^{-1}(x) = \frac{x - 65}5[/tex]
B.
[tex]f(t) = 3.5 - 0.5t \to t = 3.5 - 0.5f^{-1}(t)\\\\t = 3.5 - 0.5f^{-1}(t)\\t - 3.5 = -\frac12f^{-1}(t)\\f^{-1}(t) = 7 - 2t[/tex]
C.
[tex]P(n) = \frac n3 -1.2\to n = \frac{P^{-1}(n)}3-1.2\\\\n = \frac{P^{-1}(n)}3-1.2\\n + 1.2 = \frac{P^{-1}(n)}3\\P^{-1}(n) = 3n + 3.6[/tex]
