Download Find Inverse Switch X and Y Notes

9-5
Functions and Their Inverses
To find the inverse of a function
• Switch the x and y
• Solve for y
Holt Algebra 2
9-5
Functions and Their Inverses
Example 1
Means the
inverse of g(x)
Holt Algebra 2
3
y x
4
9-5
Functions and Their Inverses
Example 2
Means the
inverse of g(x)
Holt Algebra 2
y  9x  5
9-5
Functions and Their Inverses
Example 2 Continued
Step 1 Find the inverse.
Rewrite the function using y instead of f(x).
Switch x and y in the equation.
Cube both sides.
Simplify.
Isolate y.
Holt Algebra 2
y 1  x3  1
9-5
Functions and Their Inverses
Check It Out! Example 2 Continued
Step 1 Find the inverse.
y = x3 – 2
Rewrite the function using y instead of f(x).
x = y3 – 2
Switch x and y in the equation.
x + 2 = y3
Add 2 to both sides of the equation.
3
3
3
x+2= y
3
x+2=y
Holt Algebra 2
Take the cube root of both
sides.
Simplify.
y 1  3 x  2