Inverses
f(x)=root(5)(x+3
f-1(x)=
x^5-3
g(a)= 2a-4
f(a)= -2a+2
Find (g o f)(-2)
-4a
8
What transformations are happening?
g(x)=-1/2sqrt(x+3)-7
Vertical compression by 1/2, left 3, down 7, reflection over the x-axis
Write the cube root function equation that has a vertical stretch by 3, right 6, and up 5
g(x)=3root(3)(x-6)+5
4=sqrt(18x)-2
x=2
f(x)=-2+(x-2)^3
f-1(x)=
root(3)(x+2)+2
g(x)= 4x-2
h(x)= x2+4
Find (g o h)(2)
4x2+14
30
Write the square root function equation for a horizontal stretch by 4, left 6, and up 5
f(x)= sqrt(1/4(x+6)) +5
What transformations are happening?
f(x)= root(3)(-1/3x-4)-9
Horizontal stretch by 3, right 4, down 9, reflection over the y-axis
9=3sqrt(n-8
n=17
f(x)=(3x+12)/7
f-1(x)=
7/3x-4
g(x)= 4x - 4
f(x)= x2 - 4x
Find (g o f)(2)
4x2-16x-4
-20
g(x)=-1/2sqrt(x+3)-7
What are the reference points for this square root function?
(0,0)-->(-3,7)
(1,1)-->(-2,-7.5)
What are the reference points for this cubic functions?
g(x)=3root(3)(x-6)+5
(-1,-1)-->(5,2)
(0,0)-->(6,5)
(1,1)-->(7,8)
k=sqrt(20-k
x=-5, x=4
f(x)=-7/3x-13/3
f-1(x)=
-3/7x-13/7
g(x)= -3x2-1
f(x)= a-2
Find (f o g)(9)
-3a2+12a-13
-148
What are the reference points for this square root function?
f(x)=sqrt(1/4(x+6))+5
(0,0)-->(-6,5)
(1,1)-->(-2,6)
f(x)= root(3)(-1/3x-4)-9
What are the reference points for this cubic function?
(-1,-1)-->(7,-10)
(0,0)-->(4,-9)
(1,1)-->(1,-8)
x-3=sqrt(7x-27)
x=9, x=4
f(x)=sqrt((-x+2)/2)
f-1(x)=
-2x^2+2
f(x)= x2+2x
g(x)= 3x+5
Find (f o g)(-5)
9x2+36x+35
80
Write the equation for the square root function (b)reference points shown:
(0,0)-->(1,2)
(1,1)-->(0,3)
f(x)=sqrt(-(x-1))+2
Write the equation for the cube root function (a)reference points shown:
(-1,-1)-->(3,4)
(0,0)-->(4,2)
(1,1)-->(5,0)
f(x)=-2root(3)(x-4)+2
x=-5+sqrt(6x+37)
x=2, x=-6