SOLUTION: consider the function f(x)=x^3-4 and g(x)=3 sqrt x+4 a. find f(g(x)) b. find g(f(x)) c. determine whether the functions f and g are inverses of each other

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: consider the function f(x)=x^3-4 and g(x)=3 sqrt x+4 a. find f(g(x)) b. find g(f(x)) c. determine whether the functions f and g are inverses of each other       Log On


   

Question 838749: consider the function f(x)=x^3-4 and g(x)=3 sqrt x+4
a. find f(g(x))
b. find g(f(x))
c. determine whether the functions f and g are inverses of each other

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
see the following:
$$$$$
f(g(x)) = x and g(f(x) = x
this makes f(x) and g(x) inverse functions of each other.
to find the inverse of x^3 - 4, do the following:
start with:
y = x^3 - 4
replace x with y and y with x to get:
x = y^3 - 4
solve for y by doing the following:
add 4 to both sides of the equation to get:
x + 4 = y^3
take the cube root of both sides of the equation to get:
cube root of (x + 4) = y
commute this equation to get:
y = cube root of (x + 4) which looks like y+=+root%283%2Cx%2B4%29 when sent through the algebra.com formula generator.
y+=+root%283%2Cx%2B4%29 is the same as g(x).
they are both inverse functions to f(x).