Question

If f(x) = 5x + 18, then f-1(x) = _________.f-1(x) = -x + 18/5f-1(x) = (x - 18)/5f-1(x) = x + 18/5f-1(x) = -x - 18/5

Answer 1

`f^(-1)(x)=(x-18)/(5)`

1) To find the inverse function of this f(x) function, we need to presume this is a bijective function, and then follow these steps all the way through it:

2)

`\begin{gathered} f(x)=5x+18 \\ \\ y=5x+18\:\:\:\:Swap\:the\:variables \\ \\ x=5y+8\:\:Isolate\:the\:y-term\:on\:the\:left\:side \\ \\ 5y+18-18=x-18\:\:\:Subtract\:18\:from\:both\;sides \\ \\ 5y=x-18\:\:\:Divide\:both\:sides\:by\:5 \\ \\ (5y)/(5)=(x)/(5)-(18)/(5)\:\:\:Simplify: \\ \\ y=(x-18)/(5)\:\:\:Write\:the\:proper\:notation \\ \\ f^(-1)(x)=(x-18)/(5) \end{gathered}`

Thus, this is the answer.