Operations on Functions
Inverses
Exponentials
Logarithms
Systems of Equations
100
Given F(x) = 3 - x and
G(x) = 5x
2
, find the value of
(F + G)(-2)
(F + G)(-2) = 25
100
If g(-2) = -5, then
g
-1
(-5) = _____
-2
100
Evaluate:
(
5
/
3
)
-3
27
/
125
100
Simplify
log 10
4
4
100
Convert the following system to a matrix:
3x + 5y + 4z = 2
5x + 3z = 1
x = 6
200
Given the functions
h(x) = 3 - x
2
and
v(x) = 8x, find the value of
(v ○ h)(2)
-8
200
Draw the graph of two different functions, with the conditions:
A. function IS one-to-one
B. function is NOT one-to-one
A. passes Horizontal Line Test
B. does not pass Horizontal Line Test
200
Write the given exponential in logarithmic form:
8
x
= 16
log
8
16 = x
200
Use the Change of Base to find the decimal value of log
5
12, rounded to the nearest hundredth.
log 12
/
log 5
= 1.54
200
Solve
x = 2y + 5
3x - 5y = 12
(-1, -3)
300
Find the difference quotient
(f(x+h) - f(x))
/
h
of the function
f(x) = 2x + 1
(2(x+h) + 1) - (2x + 1)
/
h
(2x + 2h + 1 - 2x - 1)
/
h
2h
/
h
2
300
Simplify
5
log
5
(x-3)
(x-3)
300
Sketch the graph of
f(x) = 4
x
+ 1
300
Find the domain of
log(9-3x)
(-∞, 3)
300
Graph the solution:
y > -3x + 5
y ≤ x - 2
400
Given y(x) = 9x + 2 and
q(x) = x
5
, find the function
(q ⋅ y)(x) and its domain
(q ⋅ y)(x) = (9x + 2)(x
5
) = 9x
6
+ 2x
5
domain: (-∞, ∞)
400
Find the inverse of the one-to-one function
h(x) = 8x - 3
h
-1
(x) =
x+3
/
8
400
Solve
3
6x
= 9
x+2
x = 1
400
Solve
ln(x - 4) = 3
x = e
3
+ 4
400
Solve the system:
4x - 3y = 7
-8x + 6y = 1
No Solution
500
Given k(x) = 7√x and
m(x) = 5x - 1, find the function
(k ○ m)(x) and its domain.
(k ○ m)(x) = 7√(5x-1) domain: [
1
/
5
, ∞)
500
Determine algebraically if the function
g(x) = 2x
2
- 12 is a one-to-one function
g(a) = g(b)
2a
2
- 12 = 2b
2
- 12
2a
2
= 2b
2
a
2
= b
2
a = ± b
500
Solve the following, giving both exact and decimal answers
5
x-3
= 2
-1
x =
(3ln5 - ln2)
/
ln5
= 2.57
500
Solve
log
3
(x - 5) - log
3
(x) = log
3
(2)
No Solution
500
Solve the system:
3x - y + 2z = 4
2y - 4z = 1
-x + y - 2z = -1
(
3
/
2
, 2z + ½, z)
Continue
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