b Choose an input number for the function f(x) and evaluate.
A
a f^(- 1)(x)=x+2/7
B
b See solution.
Practice makes perfect
a Before we can find the inverse of the given function, we need to replace f(x) with y.
f(x)=7x-2 ⇔ y=7x-2Now, to algebraically determine the inverse of the given equation we exchange x and y and solve for y.
Given Equation & Inverse Equation
y=7 x-2 & x=7 y-2
The result of isolating y in the new equation will be the inverse of the given function.
Finally, we write the inverse of the given function in function notation by replacing y with f^(- 1)(x) in our new equation.
f^(- 1)(x)=x+2/7
b We want to show that the inverse function found in Part A is correct. To do this, we will choose an input number for the function f(x) and evaluate. Let's choose x= 1 and calculate f( 1).
