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)?

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) (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.

RELATED QUESTIONS
Please show work. Consider the functions: f(x)=x^2+4 g(x)=x a Find f(g(x)) b... (answered by rothauserc)

Consider the functions: f(x)=x^2+4 g(x)=x Find f(g(x)) f(g(1)) find f(2g(x)) (answered by MathLover1)

Please show work. Consider the functions: f(x)=x^2+4 g(x)=x a. Find f(g(x)) (answered by Fombitz)

Please show work. Consider the functions: f(x)=x^2+4 g(x)=x a. Find f(g(x))... (answered by fractalier)

Consider the function f(x)=3x-6 and g(x)=x/3+2. A) Find f(g(x)). B) Find g(f(x)). C)... (answered by ReadingBoosters)

Please show all work. Given the following functions f(x)=x+3 g(x)=√(x-1)... (answered by rothauserc)

I so badly need someones help asap. I have 6 problems i really need help with. Can... (answered by Alan3354)

Show work please. consider the functions f(x)=4x-16 and g(x)= x/4 +4. Find f(g(x)) and... (answered by josgarithmetic)

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)) (answered by Theo)