Answer:
Step-by-step explanation:
<u>Composite Function</u>
Given f(x) and g(x) as real functions, the composite function is defined as:
It can be found by substituting g into f.
We are given the functions:
f(x) = -x + 3
g(x) = -x -1
Find
Removing parentheses:
Simplifying:
The difference of two squares factoring pattern states that a difference of two squares can be factored as follows:
So, whenever you recognize the two terms of a subtraction to be two squares, you can factor it as the sum of the roots multiplied by the difference of the roots.
In this case, the squares are obvious: is the square of
, and
is the square of
So, we can factor the expression as
(the round parenthesis aren't necessary, I used them only to make clear the two terms)
We can simplify the expression summing like terms:
Answer-
<em>The inverse of is </em>
<u>Solution-</u>
The given function is,
We can get the inverse by interchanging he variable x and y among themselves and then separating each variables.
So in the inverse would be,
Taking log of both sides,
As,
Applying the same,
As,
Applying the same,
Therefore, the inverse of is
.