a Before we can find the inverse of the given function, we need to replace f(x) with y.
f(x)=x/3-2 ⇔ y=x/3-2Now, to algebraically determine the inverse of the given equation we exchange x and y and solve for y.
Given Equation & Inverse Equation
y=x/3-2 & x=y/3-2
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)=3x+6
b Before we can find the inverse of the given function, we need to replace g(x) with y.
g(x)=1/2x+5 ⇔ y=1/2x+5Now, to algebraically determine the inverse of the given equation, we exchange x and y and solve for y.
Given Equation & Inverse Equation
y=1/2 x+5 & x=1/2 y+5
The result of isolating y in the new equation will be the inverse of the given function.
