Rational Exponents/Properties
Function Operations & Composition
Inverse Functions
Graph Square Root
Solve Radical Equations
100
convert to radical form. x^2/3
cubed root of x^2
100
Given f(x) = 5x, g(x) = x + 2. Find f(g(2))
20
100
Looking at the tables. Do these represent inverses? x/y x/y 0,6 6,0 1,4 4,1 2,2 2,2 3,0 0,3
Yes!
100
Domain and range of square root of (x+4)
D: x greater then or equal to -4 R: y greater then or equal to zero
100
Solve for x: (4x+9)^(1/2) =5
x=4
200
7^(1/4) * 7^ (1/2)
7^(3/4) *Common base - add exponents
200
f(x) = 3x -8 and g(x) = 2x^2. Find the following. g(f(5))
g(f(5)) = 98
200
f(x) =x^2. Is f(x) a function? Is f^-1 (x) a function?
f(x) is a function bc f(x) passes the VLT f^ -1 (x) is not a function bc f(x) does not pass HLT
200
State the domain & range. y = (x+6)^(1/2)+2
Domain: x greater then or equal to -6 Range: y greater then or equal to 2
200
Solve for x: x + 1 = (7x+15)^(1/2).
The only solution is 7. -2 is extraneous.
300
(64y^6)^(1/3)
4y^2 (4.4.4.y.y.y.y.y.y)^(1/3) Look for sets of 3 4.y.y = 4y^2
300
f(x) = 4x and g(x) = 5x - 2 Find g(f(x))
20x-2
300
Find an equation for the inverse of the relation y =3x - 5
y = 1/3 x + 5/3 bc. x = 3y -5 x + 5 = 3y 1/3 x + 5/3 = y
300
State the Domain & Range. y = -2(x-3)^(1/2) + 2
Domain: x is greater or equal to 3. Range: y is less than or equal to 2.
300
Solve (2x + 7)^(1/3) = 3.
x = 10 bc. ((2x + 7)^(1/3))^3=3^3 2x + 7 = 27 2x = 20 x =10
400
Simplify the square root of (32x^8)
4x^4 root{2}
400
Create two functions such that f(g(4))=0
f(x)=x-9 g(x)=x+5
400
Find the inverse of f(x) = -10x^3
f^-1 (x) = ( x/-10)^(1/3)
400
Domain and range of y = (3x+4)^(1/2) -1
Domain: x greater then or equal to -4/3 Range: y greater then or equal to -1
400
Solve. (2x-7)^(1/2)= (x + 2)^(1/2)
x=9
500
(-16)^(3/4) has how many real solutions
None
500
f(x)=x-4 g(x)=x^2-10 Find domain & range of f(g(x))
D: all real numbers R: y greater then or equal to -14
500
f(x)=4x^2 g(x)=2x^0.5
No! f(g(x))=16x not x
500
domain and range of y=-2(x+3)^(1/2)-1
Domain: x greater then or equal to -3 Range: y less then or equal to -1
500
Solve: (x+5)^(1/4)=-4
no real solutions
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