SOLUTION: Hi I am stumbled with this problem: Find the inverse function g of the given function, and state the domain and range of g. y = f(x) = (x+2)^3

Algebra ->  Functions -> SOLUTION: Hi I am stumbled with this problem: Find the inverse function g of the given function, and state the domain and range of g. y = f(x) = (x+2)^3       Log On


   

Question 111761This question is from textbook College Algebra
: Hi I am stumbled with this problem:
Find the inverse function g of the given function, and state the domain and range of g.
y = f(x) = (x+2)^3






This question is from textbook College Algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
y=%28x%2B2%29%5E3 Start with the given equation


x=%28y%2B2%29%5E3 Switch x and y

Now let's solve for y


root%283%2Cx%29=y%2B2 Take the cube root of both sides


root%283%2Cx%29-2=y Subtract 2 from both sides


So our inverse function is g%28x%29=root%283%2Cx%29-2


Now if we graph, we get



So we can see that the domain and range of g is all real numbers (for both of them)