a Before we can find the inverse of the given function, we need to replace f(x) with y.
f(x)=2x+3 ⇔ y=2x+3Now, to algebraically determine the inverse of the given equation we exchange x and y and solve for y.
Given Equation & Inverse Equation
y=2 x+3 & x=2 y+3
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-3/2
b Before we can find the inverse of the given function we need to replace g(x) with y.
g(x)=x-5/4 ⇔ y=x-5/4Now, to algebraically determine the inverse of the given equation we exchange x and y and solve for y.
Given Equation & Inverse Equation
y=x-5/4 & x=y-5/4
The result of isolating y in the new equation will be the inverse of the given function.
