The Basics
When you find the inverse, what happens to the x and y variables? Give an example:
x and y switch. So (4,-3) becomes (-3,4)
Find the inverse:
f(x)=x^2,x>=0
f^-1(x)=sqrt(x)
Find the inverse:
f(x)=x^3
f^-1(x)=root(3)(x)
Rewrite the composition using function notation:
(fog)=
f(g(x))=
When you take the composition of two functions what are you doing?
Combing the functions. Using one function as the input.
f(g(x)) where g(x) is the input
When graphing the inverse, what equation is it reflected over?
y = x
Find the inverse:
f(x)=x^2+4,x>=0
f^-1(x)=sqrt(x-4)
Find the inverse:
f(x)=x^3+4
f^-1(x)=root(3)(x-4)
Find the composition f(g(x)):
f(x)=2x-9
g(x)=-5x+6
f(g(x))=-10x+3
Because we cannot take the root of a negative numeber.
taking the square root
Find the inverse:
f(x)=2/3x^2+3,x>=0
f^-1(x)=sqrt(3/2(x-3)
FInd the inverse:
f(x)=2x^3+8
f^-1(x)=root(3)((x-8)/2)
Rewrite the composition f(g(x))=
f(x)=2x
g(x)=x^2 +4
f(g(x))=2x^2+8
f(g(x))=2(x^2+4)
Do you have to restrict the domain for a cubic function?
No! you can take the cue root of a negative!
What is the inverse of cubing a number?
Taking the cube root
Find the Inverse:
f(x)=(x+2)^2,x>=0
f^-1(x)= sqrt(x)-2
Find the inverse:
f(x)=(x-5)^3+2
f^-1(x)=root(3)(x-2)+5
Find the composition g(f(x)):
f(x)=x^2-4
g(x)=6x+2
f^-1(x)=6x^2-22
How do you get the cube root on a calculator?
math, option 4
When you take the composition of a function and its inverse what should it equal?
x
Find the inverse:
f(x)=(3x-9)^2,x>=0
f^-1(x)=1/3sqrt(x)+3
Find the Inverse:
f(x)=1/3x^3-9
f^-1(x)=root(3)(3x+27)
Find the composition f(g(x)):
f(x)=x^2-4
g(x)=6x+2
f^-1(x)=36x^2+24x
What are the steps to finding the inverse of a function?
step 1: change f(x) to y
step 2: solve for x using inverse order of operations
step 3: switch x and y
step 4: rewrite using function notation
f^-1(x)=