College Algebra Examples Section 3.7
Inverses

5) Find the inverse of the function f whose rule is f(x) = 6x.

Solution: The function f multiplies domain elements by 6.
To "undo" this multiplication by 6, the inverse of f must be a function which divides by 6.
Therefore the rule for the inverse f ^-1 will be
                      

6) Find the inverse of the function f whose rule is .
Solution:  The function f multiplies domain elements by .   
To "undo" this multiplication by , the inverse of f must be a function which multiplies by 3..
Therefore the rule for the inverse f ^-1 will be f ^-1(x) = 3x.

10) Find the inverse of the function f whose rule is .
Solution:  This function subtracts 1 from domain elements and then divides that difference by 5.
To "undo" these two operations, the inverse of f must multiply by 5 and then add 1 to that product.
Therefore the rule for the inverse f ^-1 will be .

13) Show that the functions f and g are inverses of each other.
Their rules are: f(x) = 2x and .
Solution:


Therefore the functions f and g are inverses of each other.

16) Show that the functions f and g are inverses of each other.
Their rules are f(x) = 3 - 4x   and   
Solution:


Therefore the functions f and g are inverses of each other.

17)  Show that the reciprocal function whose rule is is its own inverse.
Solution:
To verify that f is its own inverse we must show that

Therefore f is its own inverse.

24)  Show that the functions f and g are inverses of each other.

Solution:


Therefore the functions f and g are inverses of each other.