SOLUTION: Consider the functions: f(x)=x^2+4 g(x)=x Find f(g(x)) f(g(1)) find f(2g(x)) What is the inverse of f(x)? What is the inverse of g(x)? Can Someone please help

Algebra ->  Functions -> SOLUTION: Consider the functions: f(x)=x^2+4 g(x)=x Find f(g(x)) f(g(1)) find f(2g(x)) What is the inverse of f(x)? What is the inverse of g(x)? Can Someone please help      Log On


   

Question 1021484: Consider the functions:
f(x)=x^2+4
g(x)=x
Find f(g(x))
f(g(1))
find f(2g(x))
What is the inverse of f(x)?
What is the inverse of g(x)?
Can Someone please help me with this question. I am supposed to provide the calculations.
Thanks
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=x%5E2%2B4
g%28x%29=x

f%28g%28x%29%29=f%28x%29=x%5E2%2B4
f%28g%281%29%29=f%281%29=1%5E2%2B4=5
f%282g%28x%29%29=f%282x%29=%282x%29%5E2%2B4=4x%5E2%2B4

the inverse of f%28x%29:If f had an inverse, then its graph would be the reflection of the graph of f about the line y+=+x.
since f%28x%29=y we have
y=x%5E2%2B4............swap x and y
x=y%5E2%2B4.........solve for y
x-4=y%5E2
y=sqrt%28x-4%29
so, the inverse is f%5E-1%28x%29=sqrt%28x-4%29

the inverse of g%28x%29=x is
g%5E-1%28x%29=x