Composite Functions
Given f(x)=3x-1 and g(x)=3-x^2.
Find f(g(5)).
Find f(g(x)).
Find g(f(x)).
f(g(5))=-67
f(g(x))=8-3x^2
g(f(x))=-9x^2+6x+2
Given that f(x)=2x+3 and g(x)=x^2, find(f o g) (2).
(f o g) (2)=11
Given f(x)=3x+2, find the inverse.
Inverse=(x-2)/3
You got it!
Who is somebody that is good at helping others?
Answer to get 100 points.
Given f(x)=1/x-4 and g(x)=1/x, find f(g(x)) and its domain.
f(g(x))= 1
______
(1/x)-4
Domain: (-oo, 0) U (0, 4) U (4, oo)
Given that f(x)=3x-1 and g(x)=x+5, find (f o g) (x).
(f o g) (x)=3x+14
Verify if this function and its inverse works:
f(x)= (x-4)/5
Yes.
Verify that this function is an inverse of itself.
f(x)=(x+12)/2
Call someone out who laughs at their own jokes.
Answer for 200 points.
Write h(x)=√(3-x^2) as the composition of two functions, f(x)≠x and g(x)≠x, such that h(x)=f(g(x)).
Answers will vary.
Given these values, find (f o g) (2).
f(1)=4
f(4)=2
g(2)=1
g(3)=2
(f o g) (2)= 4
Given that f(x)=(2x-5)/3, find the inverse, and verify it.
List the 4 steps in order to solve an inverse function.
1. Replace f(x) with y.
2. Solve for x in terms of y.
3. Interchange x and y.
4. Replace y with f^-1(x)
Who has a pretty good sense of fashion?
Answer for 300 points.
Use the function f(x)=4x+5 to evaluate: f(x+h)-f(x)/h.
3
Given f(x)=1/(x+1) and g(x)=x^2-4, find (f o g) (x) and its domain.
(f o g) (x)=1/(x^2-3)
Domain: (-oo, -√3)U(-√3, √3)U(√3, oo)
What are the inverse values (write in inverse notation).
1-->3
f(x)={ 2-->5
4-->7
f^-1(3)=1
f^-1(5)=2
f^-1(7)=4
Does every function have an inverse?
No, only one-to-one functions have inverses, unless you add restrictions.
Who would join a math cult and love it?
Answer for 400 points.
Given f(x)=√(4-x) and g(x)=1/x-2, find the domain for f(g(x)).
(-oo, 2) U (2, 2.25]
Solve the inequality: |x+1|>-2
N/A
Find the inverse of this function:
f(x)=(6+4x)/(3-5x)
The y=x line.
Answer for 500 points.