Answer:
Explanation:
a) We want to find the inverse of the function f(x)
We have this as follows:
[tex]\begin{gathered} \text{ f(x) = 3x} \\ \text{set f(x) as y} \\ y\text{ = 3x} \\ x\text{ = }\frac{y}{3} \\ f^{-1}(x)\text{ = }\frac{x}{3} \end{gathered}[/tex]
b) We want to verify that the functions are inverses of each other
We can do this by using a composite relationship
[tex]\text{ f(f}^{-1}(x))\text{ = f(}\frac{x}{3})\text{ = 3}\times\frac{x}{3}\text{ = x}[/tex][tex]\text{ f}^{-1}(f(x))=f^{-1}(3x)\text{ = }\frac{3x}{3}\text{ = x}[/tex]
As we can see:
[tex]f(f^{-1}(x))=f^{-1}(f(x))\text{ = x}[/tex]
The inverse works for all real numbers and thus, we have it as:
[tex]\text{ f}^{-1}(x)\text{ = }\frac{x}{3}\text{ , for all x}[/tex]
