Operations on Functions
If f(x) = x + 5 and g(x) = x - 4, find (f + g)(x)
2x + 1
What is the inverse of the relation?
A = {(3, 1), (4, -3), (8, -3), (9, 0)}
A'= {(1, 3), (-3, 4), (-3, 8), (0, 9)}
Is the domain of a square root function always all real numbers?
Never
solve: (the square root of x) -1 = 4
x = 25
Who won the Super Bowl?
Eagles
If f(x) = x + 5 and g(x) = x - 4, find (f - g)(x)
9
Find the equation of the inverse of f(x) = 3x
f-1(x)= x/3
Describe the transformation of the following graph: y = (sqrt of x) + 3
up 3
Solve: (square root of x - 5) = 4
x = 21
The approximate time in t seconds that it takes an object to fall a distance of d feet is given by t=sqrt(d/16). How far will the object fall in 8 seconds?
1024 feet
If f(x)= x + 5 and g(x) = x - 4, find (f * g)(x)
x2 + x - 20
Find the inverse of f(x) = 2x - 1 and graph both equations.
f-1(x) = (x - 1)/2 or
f-1(x) = (1/2)x - 1/2
Describe the transformations of the following: y = -(sqrt x - 3)
reflected over x axis
right 3
solve: v1/2 + 1 = 4
v = 9
Find f(g(x)):
f(x)=(-4,-5), (0,3), (1,6)
g(x)=(6,1), (-5,0), (3,-4)
(6,6),(-5,3),(3,-5)
If g(x) = -3x and h(x) = 4x - 1, find g[h(x)] AND h[g(x)].
g[h(x)]= -12x + 3
h[g(x)] = -12x - 1
Find the inverse of the function and graph both.
f(x) = (1/4)x
f-1(x) = 4x
Describe the graph of the following and give the domain and range.
y = -(sqrt x + 2) - 1
reflected over x-axis
left 2
down 1
D: [-2, infinity) R: (-infinity, -1]
Solve: 10 - (square root of 2x) = 5
x = 12.5
Are the following functions inverses?
g(x)=2x+9
f(x)=1/2x-9
No
If f(x) = 3x, g(x) = x + 4 and h(x) = x2 - 1,
find h[f(-3)]
80
Find the inverse of the function and then graph both.
f(x) = (1/6)x + 3
f-1= 6x - 18
Describe the graph of the following and give the D and R in interval notation.
y = 2(sqrt x - 5) + 3
stretched vertically by 2
right 5
up 3
D: [5, infinity) R: [3, infinity)
Solve: 2 times [the square root of (3x + 4)] + 1 = 15
x = 15
Find f(f(x))
f(x)=3x+4
9x+16