Basics
f(x)=2x
g(x)=x+4
f(x) o g(x)
What is 2x+8
Is this function one-to-one?
f(x) = 2x
g(x) = x+5
f(x) o g(x)
What is “yes”?
Q: What is the domain of f o g?
f(x)=x^2+3x-1
g(x)=2x+3
A: all real numbers
f(x) = 3x+2
f-1 = ?
what is “f-1 = (x-2)/3”
f(x)=5x
g(x)=x^2+3
g(x) o f(x)
25x^2+3
Is this function one-to-one?
f(x) = x^2
g(x) = 3x+4
g(x) o f(x)
What is “no”?
Q: What is the domain of f o g?
f(x)=1/(x+2)
g(x)=4/(x-1)
The domain of f o g is {x|x =/ -1, x =/ 1}
f(x) = 4x
f-1(f(2x))
What is “2x”
f(x)=4x+6
g(x)=x^2+7
g(x) o f(x)
What is 16x^2+48x+36
Is this function one-to-one?
f(x) = 2x^3+6
g(x) = x+4
f(x) o g(x)
What is “yes”?
What is the domain of f o f?
f(x) = 1/x+2
The domain of f o f is {x|x =/ -5/2, x =/ -2}
f(x)=2x+2
g(x)= 3x+3
g-1(g(f(3)))
What is “8”
f(x)=12x+5
g(x)=3x^2+4x+9
g(x) o f(x)
432x^2+408x+54
Is this function one-to-one?
f(x)=x^3-x
g(x)=2x-1
f(x) o g(x)
What is “yes”
What is the domain of f o g?
f(x) = (x+2)/(x-1) g(x) = (x+1)/(x+4)
{x|x doesn’t equal -4}
f(x) = 4x-3
g(x) = 2x+3
g-1(f(g(4)))
What is “19”
f(x)=3x^2+6x+4
g(x)=(6x^2+3)(3x+8)
g(x) o f(x)
What is 486x^6+2916x^5+10152x^4+17280x^3+17595x^2+7542x+1980
f(x)=(x−2)^2(x+1)
g(x)=−3x+4
g(x) o f(x)
What is “no”
find f[g(x)] and determine the domain
f(x) = 4/(x+2) g(x) = 1/x
{x|x doesn’t equal -(½), 0}
f(x) = 9x-51
g(x) = 13x+1
f-1(g(f(7)))
What is “23.11… or 208/9”