Problem 1 :
The volume of a balloon is given by the equation
V = t^{2} - 3t + 3
What is the volume of the balloon after 3 seconds ?
a) 3 b) 6 c) 9 d) 12
Solution :
V = t^{2} - 3t + 3
When t = 3
V = 3^{2} - 3(3) + 3
V = 9 - 9 + 3
V = 3
So, volume of balloon after 3 seconds is 3.
Problem 2 :
x 1 2 h |
f(x) 0 h k |
In the table above, if f(x) = x^{2} + x - 2, what is the value of k ?
Solution :
f(x) = x^{2} + x - 2
When x = 2, f(2) = h
f(2) = 2^{2} + 2 - 2
h = 4
When h = 4, f(4) = k
f(4) = 4^{2} + 4 - 2
k = 16 + 4 - 2
k = 18
Problem 3 :
Rocket Rocket 1 Rocket 2 Rocket 3 Rocket 4 Rocket 5 Rocket 6 Rocket 7 |
Fuel burned (liters) 7 12 17 23 29 32 35 |
The distance d, in meter traveled by a rocket depends on the amount of fuel f, in liters. It burns according to the equation
d = (2/3) f
Based on the table above, how many rockets traveled more than 20 meters ?
a) One b) Two c) Three d) Four
Solution :
d = (2/3) f
when f = 7 d = (2/3) (7) d = 14/3 (< 20) |
when f = 23 d = (2/3) (23) d = 15.3 (< 20) |
when f = 29 d = (2/3) (29) d = 19.3 (< 20) |
When f = 32
f = (2/3)(32)
f = 21.3 > 20
For f = 32 and f = 35, the value of f will be greater than 20. So, answer is 2.
Problem 4 :
Let the function f be defined by f(x) = 2x^{3} - 1 and let the function g be defined by g(x) = x^{2} + 3, what is the value of f(g(1))?
a) 4 b) 23 c) 56 d) 127
Solution :
f(x) = 2x^{3} - 1
g(x) = x^{2} + 3
g(1) = 1^{2} + 3 ==> 4
f(g(1)) = f(4) = 2(4)^{3} - 1
= 2(64) - 1
= 128 - 1
= 127
So, option D is correct.
Problem 5 :
x 1 2 3 4 |
f(x) 4 6 5 2 |
g(x) 0 2 6 4 |
Four values for the function f and g are shown in the table above. If g(m) = 6, what is the value of f(m) ?
Solution :
For g(3), we get 6. So, g(m) = 6. Then value of m is 3.
f(3) = 5
Problem 6 :
f(x) = ax^{3} + b
In the function f defined above, a and b are constants. If f(-1) = 4 and f(1) = 10, what is the value of b ?
Solution :
f(x) = ax^{3} + b
f(-1) = a(-1)^{3} + b 4 = -a + b ------(1) |
f(1) = a(1)^{3} + b 10 = a + b ------(2) |
(1) + (2)
-a + b + a + b = 4 + 10
2b = 14
b = 7
Applying the value of b in (1), we get
-a + 7 = 4
-a = 4 - 7
-a = -3
a = 3
Problem 7 :
For all x ≥ 3, f(x) = √(x-3)/2 .If f(n) = 3 is the value of n ?
Solution :
f(x) = √(x-3)/2
If f(n) = 3,
f(n) = √(n-3)/2
3 = √(n-3)/2
Multiplying by 2 on both sides.
3(2) = √(n - 3)
6 = √(n - 3)
Take square on both sides, we get
36 = n - 3
n = 36 + 3
n = 39
Problem 8 :
Let the function f be defined by f(x) = x^{2} - x + 3. If f(m + 1) = 5 and m > 0. What is the value of m ?
Solution :
f(x) = x^{2} - x + 3
f(m + 1) = 5
f(m + 1) = (m+1)^{2} - (m+1) + 3
5 = m^{2} + 2m + 1 - m - 1 + 3
5 = m^{2} + m + 3
m^{2} + m + 3 - 5 = 0
m^{2} + m - 2 = 0
(m + 2)(m - 1) = .0
Equating each factor to 0, we get
m = -2, m = 1
Problem 9 :
f(x) = x^{3} + 2
g(x) = 2x
The functions f and g are defined above. If f(b) = 29, what is the value of g(b) ?
a) 4 b) 6 c) 8 d) 10
Solution :
f(x) = x^{3} + 2
f(b) = 29
f(b) = b^{3} + 2
29 = b^{3} + 2
b^{3 }= 29 - 2
b^{3 }= 27
b = 3
Applying the value of b in g(x)
g(b) = g(3) = 2(3)
g(3) = 6
Problem 10 :
If f(x) = √(x + 1), what is f(x^{2} + 4) equal to ?
a) x + 3 b) x + 5 c) √(x^{2} + 4) + 1 d) √(x^{2} + 4x) + 1
Solution :
f(x) = √(x + 1)
f(x^{2} + 4) = √(x^{2} + 4 + 1)
So, option c is correct.
Feb 25, 24 07:44 AM
Feb 24, 24 11:07 PM
Feb 24, 24 08:49 PM