Graphing Square/Cubic Roots
The transformations of the square root function
2*root(2)(x+5) - 4
are:
Vertical Stretch of 2
Translation of 5 units to the left
Translation of 4 units down
Solve the equation:
root(3)(x) - 10 = -7
& check for extraneous solutions.
x = 27
Simplify.
(root(3)(x))/(root(6)(x^5))
(sqrt(x))/x
121/2
2 (sqrt) 3
Functions that undo each are called:
Inverse Functions
The domain and range of
(1/2)*root(3)(x+6)
is:
D: all real numbers
R: all real numbers
Solve the equation:
root(2)(2x)-2/3=0
& check for extraneous solutions.
x=2/9
Let f(x) = 6x and g(x) = x^(3/4). Find (f/g)(x).
(f/g)(x) = 6x^(1/4)
501/2
5 (sqrt) 2
Find the inverse function:
f(x) = 2x^4 - 5
g(x) = root(4)((x+5)/2)
The domain and range of
root(2)(6x)+3
is:
Domain: x is greater than or equal to zero
Range: y is greater than or equal to 3
Solve the equation:
root(4)(4x)-13=-15
no real solution
Find (fg)(x) & (f/g)(x).
f(x)=2x^3, g(x) = root(3)(x)
(fg)(x) = 2x^(10/3) & (f/g)(x) = 2x^(8/3)
(25x2)1/2
5x
Find the inverse function of
f(x) = (2/3)x - 1/3
g(x)= (3x+1)/2
The transformations of the cubic root function
root(3)(-32x)+3
are:
Horizontal Shrink of a factor of 1/32
Reflection in the y-axis
Translation 3 units up
Solve the equation:
root(2)(2x+30) = x + 3
x=3
Find the (f+g)(x) & (f-g)(x).
f(x)= 6x - 4x^2 -7x^3, g(x) = 9x^2 -5x
(f+g)(x)= -7x^3 + 5x^2 + x
(f-g)(x) = -7x^3 -13x^2 + 11
(128x2y)1/2
8x (sqrt) 2y
Determine whether the inverse of f is a function. Then find the inverse.
f(x) = x^3 - 1
g(x) = root(3)(x+1)
Write a rule for g that represents the indicated transformation of f
Let g be a horizontal shrink of 2/3, followed by a translation 4 units to the left of the graph of:
root(2)(6x)
root(2)(9x+36)
Solve the equation:
root(2)(3x-8)+1 = root(2)(x+5)
x=4
Find the (f+g)(x) & (f-g)(x) of the two functions when x = 5.
f(x) = 7x^(5/3), g(x) = 49x^(2/3)
(f+g)(5) = 245.62
(f-g)(x) = -40.94
(147x3y4)1/2
7xy2 (sqrt) 3x
Determine whether the functions are inverse functions:
f(x)= (x-3)/4, g(x) = 4x +3
The functions are inverses.