SOLUTION: Please show work. Consider the functions: f(x)=x^2+4 g(x)=x a. find f(2g(x)) b. What is the inverse of f(x)? c. What is the inverse of g(x)?

Algebra ->  Functions -> SOLUTION: Please show work. Consider the functions: f(x)=x^2+4 g(x)=x a. find f(2g(x)) b. What is the inverse of f(x)? c. What is the inverse of g(x)?       Log On


   

Question 1021436: Please show work.
Consider the functions:
f(x)=x^2+4
g(x)=x
a. find f(2g(x))
b. What is the inverse of f(x)?
c. What is the inverse of g(x)?
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
a) If g(x) = x, then 2g(x) = 2x and then f(2g(x)) = f(2x) = (2x)^2 + 4 = 4x^2 + 4
b) To find an inverse, put y in for f(x). You switch x for y and solve for the new y. Then put f^-1(x) in for the new y. Like this
y = x^2 + 4
x = y^2 + 4
x - 4 = y^2
y = sqrt(x-4)
f^-1(x) = sqrt(x-4)
c) g(x) = x
y = x
x = y
f^-1(x) = x
No surprise.