Trigonometry Inverse Trigonometric Functions
Inverse Functions
   Concepts 1

Definition 
.
Let f be a one-to-one function with domain D and range R.   The inverse of f is a function   f -1 with domain R and range D for which:
f( f -1(x))= x for every x in R
and
f -1(f(x))=x for every x in D.

Statement 1
.

Finding f -1
To find f -1 for one-to-one function f:
  1. Write y instead of f(x);
  2. Interchange x and y;
  3. Solve the equation x = f(y) for y;
  4. Write f -1(x) instead of y.

Example. Given: f(x) = 3x+2. Find: formula for f -1(x).
Solution
1. y = 3x+2   Write y instead of f(x).
2. x = 3y+2   Interchange x and y.
3. 3y+2 = x   Solve the equation x = f(y) for y.
  3y = x-2    
  y =    
4. f-1(x) =   Write f -1(x) instead of y.

Statement 2
.
The graph of an inverse function can be obtained by reflecting the graph of the original function in the line y=x.

    f(x) = 3x+2


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