1. Inverse Functions
Given 2 functions, f(x) & g(x), if f(g(x))=x AND g(f(x))=x, then f(x) & g(x) are inverses of each other.
Symbols: f -1(x) means “f inverse of x”

2. Ex: Verify that f(x)=-3x+6 and g(x)=-1/3x+2 are inverses.
Meaning find f(g(x)) and g(f(x)). If they both equal x, then they are inverses.
f(g(x))= -3(-1/3x+2)+6
= x-6+6
= x
g(f(x))= -1/3(-3x+6)+2
= x-2+2
= x
** Because f(g(x))=x and g(f(x))=x, they are inverses.

3. Your Turn!
Given that f(x) = 7x  2, use composition of functions to show that f 1(x) = (x + 2)/7.
Solution:

4. To find the inverse of a function:
Change the f(x) to a y.
Switch the x & y values.
Solve the new equation for y.
** Remember functions have to pass the vertical line test!

5. To find the inverse of a function:
Change the f(x) to a y.
Switch the x & y values.
Solve the new equation for y.
** Remember functions have to pass the vertical line test!

6. Ex: Find an inverse of y = -3x+6.
Steps: -switch x & y
-solve for y
y = -3x+6
x = -3y+6
x-6 = -3y

7. Ex: g(x)=2x3
y=2x3
x=2y3
Inverse is a function!

8. Ex: f(x)=2x2-4 Determine whether f -1(x) is a function, then find the inverse equation.
y = 2x2-4
x = 2y2-4
x+4 = 2y2
f -1(x) is not a function.

9. Your Turn! f(x) = 3x2 - 4
x=3y2 - 4