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## Inverse Functions

MAKE SMALLER

 Functions - Inverse Functions - Contents

Two function are inverse functions if applying a composite function produces the original domain set of x of the first interior function. If functions f(x) and g(x) are inverse functions then f(g(x)) = x and g(f(x)) = x. To satisfy this condition the functions must have matching range and domain sets. If all this is true then the two functions are inverse functions. To create an inverse of a function y = f(x) switch the x variable for the y variable and then solve for y. The new y = g(x) is the inverse function. When mapped two inverse functions produce results that are symmetrical around the line y = x on the Cartesian Plane.

 Functions - Inverse Functions - Examples

A function:
If y = f(x) is y = 5x + 2,
y
= (5 times x) plus 2.

Switch variables:
Then x = 5y + 2.

Solve for y:
First x - 2 = 5y,
then 1/5 (x - 2) = y.

The inverse function:
y
= g(x) is y = (x - 2)/5,
y
= 1/5 times (x minus 2).

 Functions - Sections - Chapters 1 - Function Definition 2 - Function Notation 3 - Function Domain 4 - Function Range 5 - Composite Functions 6 - Inverse Functions 7 - Linear Functions 8 - Power Functions 9 - Quadratic Functions 10 - Logarithmic Functions 11 - Exponential Functions 12 - Factorial Functions 13 - Limit Functions 14 - Summation Functions 15 - Percentage Functions

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