Mixed Practice
Function Operations & Composition (6.3)
Inverse Functions (6.4)
Domain and Range
transformations
Solve Radical Equations (6.6)
100
solve: 2(x-3)^2=72
9 and -3
100
Given f(x) = 5x, g(x) = x + 2 h(x) = f(x) + g(x) = (5x)/(x+2) State the domain of h(x).
Domain: All Reals where x cannot be -2
100
Looking at the tables. Are the following inverses? x/y x/y 0,6 6,0 1,4 4,1 2,2 2,2 3,0 0,3
Yes!
100
What is the domain and range of: f(x)=1-2x^2
Domain: ALl real numbers Range y is less than or equal to 1
100
Given (4x+9)^(1/2) =5 Is x=4 a solution?
Yes. (4(4)+9)^(1/2)=5 (25)^(1/2)=5 5=5!
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 bc. f(5) = 3(5) - 8 = 7 g(7) = 2(7)^2 = 2(49) = 98
200
Use the VLT and HLT on the graph of 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
f(x)=x^3+1 Find the domain and range of the inverse
Domain: All Reals Range: All Reals
200
Given x + 1 = (7x+15)^(1/2). Are both, one, or neither of the following solutions? x = 7 or x = -2
The only solution is 7. -2 is extraneous. bc. -2 + 1 does not equal (7(-2)+15)^(1/2) -1 does not equal 1!
300
4(2x-1)^2+3=103
x=3 and -2
300
f(x) = 4x^-1 and g(x) = 5x - 2 Find f(f(x))
x. bc. f(4x^-1) = 4(4x^-1)^-1 = 4(4^-1 x) = 4^0 x= x
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
Factor completely: y^4-x^4
(y-x)(y+x)(y^2+x^2)
400
f(x)=x^2-x and g(x)= x-2 Find f(g(x))
What is x^2-5x+6
400
Find the inverse of f(x) = -10x^6 , x</ 0
f^-1 (x) = - ( x/-10)^(1/6)
400
What transformation was used to produce the graph of g(x) from the graph of f(x) f(x) = 2x^3-1 and g(x)=2x^3 +5
vertical shift up 6
400
Solve. x+1 = (7x + 15)^(1/2)
x = 7 bc. (x+1)^2 =( (7x + 15)^(1/2))^2 x^2 +2x +1 = 7x +15 x^2 -5x-14=0 (x-7)(x+2) =0 x=7 or x =-2
500
SOlve: 3x^2-10x=-5
What is x= (5+/- sqr 10)/3
500
f(x)=4x^2-4xy+x-y and g(x)= 2x^2-xy-y^2 Find (f/g)(x)
What is (4x+1)/(2x+y)
500
F(x)=2x-3 what is f^-1(-3)?
What is 0
500
The graph of y=x^2 is shifted two units left, vertically compressed by 1/2, reflected over the y-axis and shifted up 3 units. Write the equation for the transformed function
f(x)= 1/2 (-1(x+2))^2 +3
500
Simplify ((x+2)^(1/2) +1)^2
x + 2 + 2(x+2)^(1/2) + 1
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