MATH 107: Show Work for All Problems Mathematics Coursework

SHOW WORK FOR ALL PROBLEMS
1 Consider the functions:
fx=x2+4
gx=x
* Find f(g(x))
For f= x^2+4, substitute x with g(x) = x
= f(x)
=(x) ^ 2 +4
=x2+4
* f(g(1))
=f(1)= (x) ^2+ 4= (1) ^2+ 4= 1+4
= 5
* find f(2g(x))
= f (2x) = (2x^2+ 4
= 4x2 +4
* What is the inverse of f(x)?
F(x) = x2+4
Renaming f(x) as y then the equation is, y= x2+4
Then switching the and the x
X=y2+4
Y2= x-4
Y= √ x-4
Hence, f-1(x) = √ x-4
* What is the inverse of g(x)?
This is g(x) = x
Then y=x
g-1= x
2 Consider the function fx=x2-1
* What is the domain fo...