a To algebraically determine the inverse of f(x), first replace f(x) with y. Then, switch x and y and solve for y.
B
b To algebraically determine the inverse of h(x), first replace h(x) with y. Then, switch x and y and solve for y.
A
a f^(- 1)(x)=x+3/2
B
b h^(- 1)(x)= ± sqrt(x-2) + 3
Practice makes perfect
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-3
Now, to algebraically determine the inverse of the 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, to indicate that this is the inverse function of h(x), we replace y with h^(- 1)(x).
h^(- 1)(x)= ± sqrt(x-2) + 3
Note that h^(- 1)(x) is not a function. By taking the square root, we created a positive value and a negative value. This gives two
outputs for each input, and so by definition it is not a function.
