Question

Find the domain of the inverse of thefollowing functions​

Answer 1

Answer:

f(x) = (3x - 7)/5

f^-1(x) = (5y + 7)/3

The DOMAIN is the set of all possible numbers that you can put in for the independent variable and get an answer. If you had g(x) = 1/x, you could NOT put in 0 for x and get an answer because 1/0 is undefined. So the domain is all numbers but 0.

The RANGE is the set of numbers you will get for the dependent variable. If you had g(x) = 1/x, you could NOT get 0 for g(x), no matter what you put in for x. So the range is all numbers but 0.

In both your functions the domain and the range equal all possible numbers. Or all real numbers.

Step-by-step explanation:

Another way to write the answers is:

D = {x | x = R} and R = {f(x) | f(x) = R} where

D = domain, R = range, { } means set, | is such that.

Answer 2

Answer:

[-2, 4] or {-2, -1, 0, 1, 2, 3, 4}

Step-by-step explanation:

If you invert a func., it's range becomes the domain and it's domain becomes the range. So, if you want the domain of the inverted func, you'll need to find out the range of the original. That is, Domain of Inverse = Range of Original.

Range, pretty much, means the extremities bounds the y-values.

Here, for the original func., the y-extremities are -2 and +4, thus the range is [-2, 4] and hence the domain of the inverted func will be [-2, 4].