What is the answer to this question
1 answer:
You might be interested in
Start by expanding the left hand side:
which leads to
Now we want to move all terms involving the variable to the left hand side, and all constant terms on the right hand side:
Simplify both sides by summing like terms:
Divide both sides by -8 to solve for x:
Answer:
Domain of the inverse is any real number but x cannot equal zero
Domain in set builder notation =
Domain in interval notation =
================================================
Let's make h(x) be the inverse of g(x)
g(x) = 1/(x+4) is the same as y = 1/(x+4).
To find the inverse, we swap x and y, then solve for y like so....
y = 1/(x+4)
x = 1/(y+4) .... x and y swap
x(y+4) = 1
xy+4x = 1
xy = 1-4x
y = (1-4x)/x
h(x) = (1-4x)/x is the inverse of g(x)
We can verify this by showing that g(h(x)) = x and h(g(x)) = x. I'll leave that for you to confirm.
The domain of h(x) is the set of real numbers x such that x cannot be 0. So x can be anything but 0. In set builder notation, we would say and in interval notation that is
We kick out x = 0 so that (1-4x)/x doesn't have any division by zero errors.