Question

Find and solve A and B then verify if the equation is correct

Answer 1

Step-by-step explanation:

a) We want to find the inverse of the function f(x)

We have this as follows:

`\begin{gathered} \text{ f(x) = 3x} \\ \text{set f(x) as y} \\ y\text{ = 3x} \\ x\text{ = }(y)/(3) \\ f^(-1)(x)\text{ = }(x)/(3) \end{gathered}`

b) We want to verify that the functions are inverses of each other

We can do this by using a composite relationship

`\text{ f(f}^(-1)(x))\text{ = f(}(x)/(3))\text{ = 3}*(x)/(3)\text{ = x}`
`\text{ f}^(-1)(f(x))=f^(-1)(3x)\text{ = }(3x)/(3)\text{ = x}`

As we can see:

`f(f^(-1)(x))=f^(-1)(f(x))\text{ = x}`

The inverse works for all real numbers and thus, we have it as:

`\text{ f}^(-1)(x)\text{ = }(x)/(3)\text{ , for all x}`