Question

Which is not a property of an inverse function

Answer 1

Answer:

Step-by-step explanation:

Property 1

Only one to one functions have inverses

If g is the inverse of f then f is the inverse of g. We say f and g are inverses of each other.

Property 2

If f and g are inverses of each other then both are one to one functions.

Property 3

f and g are inverses of each other if and only if

(f o g)(x) = x , x in the domain of g

and

(g o f)(x) = x , x in the domain of f

Example

Let f(x) = 3 x and g(x) = x / 3

(f o g)(x) = f( g(x) ) = 3 ( x / 3 ) = x

and g o f)(x) = g( f(x) ) = (3 x) / 3 = x

Therefore f and g given above are inverses of each other.

Property 4

If f and g are inverses of each other then

the domain of f is equal to the range of g

and

the range of f is equal to the domain of g.

Example

Let f(x) = √ (x - 3)

The domain of f is given by the interval [3 , + infinity)

The range of f is given by the interval [0, + infinity)

Let us find the inverse function

Square both sides of y = √ (x - 3) and interchange x and y to obtain the inverse

f -1 (x) = x 2 + 3

According to property 4,

The domain of f -1 is given by the interval [0 , + infinity)

The range of f -1 is given by the interval [3, + infinity)

Property 5

If f and g are inverses of each other then their graphs are reflections of each other on the line y = x.

Example

Below are the graphs of f(x) = √ (x - 3)

and  its inverse f -1(x) = x 2 + 3 , x >= 0

graph of function f and its inverse

Property 6

If point (a,b) is on the graph of f then point (b,a) is on the graph