1) Describe the relationship of input and outpunt values for a composite functions.
The composition of the functions f(x) and g(x) is defined as:
(f ° g) (x) = f [g(x) ].
That means that the output of the function g(x) is the input of the function f(x).
2) Is the inverse of a function always a function?
No, the inverse of a function is not always a function.
Remember that a function cannot have two different outputs for one or more input.
The reason is that if the original function has two or more inputs that result in a same output, when you inverse the original function, the outputs of the original are the inputs of the inverse function and the inputs of the original are the outputs of the inverse. That implies that the inverse function would have some inputs related with more than one output, which is the negation of a function.
Short Answer: Tony 40 Cleo 30
Givens
T = Tony
C = Cleo
Equations
1/2 T + 1/3 C = 30 (1)
2/5 T + 1/2 C = 31 (2)
Adjustments
Multiply (1) by 3
Multiply (2) by 2
New Equations
3/2 T + C = 90 (1a)
<u>4/5 T + C = 62</u> (2a) Subtract (2a) from (1a)
(3/2 - 4/5)T = 28 the common multiple of 2 and 5 = 10.
(15/10 - 8/10)T = 28
7/10 T = 28 Multiply by 10
7T = 28*10
7T = 280 Divide by 7
T = 280/7 = 40
Put T = 40 into (1)
1/2 T + 1/3 C = 30
1/2 (40) + 1/3 C = 30
20 + 1/3 C = 30 Subtract 20 from both sides.
1/3 C = 30 - 20
1/3 C = 10 Multiply through by 3
C = 10 * 3
C = 30
Answer:
Cleo has 30 books.
Tony has 40 books.
Check
<em>Use Equation 2</em>
2/5 T + 1/2 C = 31
2/5*40 + 1/2 * 30 = ? 31
16 + 15 =?3`
31 = 31 They are equal.
The diver is 25.6 feet under sea level so they need to come back up 25.6 feet to reach sea level again. The answer is 25.6 feet.
Have a good day :)
Correct the first way is 1to1, 1:1, 1 boy to 1 girl .
