Question

x + 20The function f(x) =is one-to-one. For the function,x-5a. Find an equation for f(x), the inverse function.b. Verify that your equation is correct by showing that f(f¯¹(x)) = x and f¯1¹ (f(x)) = x.

Answer 1

Solution

Step 1:

Write the function:

f(x) = x - 5

Step 2

To find the inverse function, let f(x) = y.

a)

$\begin{gathered} y\text{ = x - 5} \\ \\ x\text{ = y + 5} \\ \\ f^{-1}(x)\text{ = x + 5} \end{gathered}$

Step 3

b)

$\begin{gathered} f(f^{-1}(x))\text{ = x + 5 - 5 = x} \\ \\ f^{-1}(f(x))\text{ = x - 5 + 5 = x} \end{gathered}$$f^{-1}(x)\text{ = x + 5 is a function of f\lparen x\rparen.}$

f