For a given function f(x) we define the domain restrictions as values of x that we can not use in our function. Also, for a function f(x) we define the inverse g(x) as a function such that:
g(f(x)) = x = f(g(x))
<u>The restriction is:</u>
x ≠ 4
<u>The inverse is:</u>
Here our function is:
We know that we can not divide by zero, so the only restriction in this function will be the one that makes the denominator equal to zero.
(x - 4)^2 = 0
x - 4 = 0
x = 4
So the only value of x that we need to remove from the domain is x = 4.
To find the inverse we try with the general form:
Evaluating this in our function we get:
Remember that the thing above must be equal to x, so we get:
From the two above equations we find:
b = 11
a = 4
Thus the inverse equation is:
If you want to learn more, you can read:
brainly.com/question/10300045
Hrcku hdxvhjgf hgdchuh bbbbb logs. Job hrvh
Here you have shared two separate functions, f(x) and g(x). You have not indicated how f and g interact. Is g supposed to be the input to f? or what?
The domains of f and g are "the set of all real numbers."
If you meant "find the domain of f(g(x))," then we're finding the domain of
3(x+1)+6, which happens to be the same as before: "the set of all real numbers."
Kindly check to ensure that you have shared ALL of the given problem.