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#1 2024-03-11 18:26:56
- mathxyz
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Property of Function
Some functions f have the property f(a + b) = f(a) + f(b) for all real numbers a and b. Which of the following functions have this property?
A. h(x) = 2x
B. F(x) = 5x - 2
C. g(x) = x^2
D. G(x) =1/x
The greatest truth about the Rapture is not its timing but it's reality.
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#2 2024-03-11 20:50:36
- Bob
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Re: Property of Function
f(a + b) = f(a) + f(b) ?
Let's try B as an example.
B. F(x) = 5x - 2
F(a) = 5a - 2 F(b) = 5b - 2 F(a+b) = 5(a+b) - 2 = 5a + 5b - 2
So, is F(a) + F(b) equal to F(a+b) ?
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob 
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#3 2024-03-12 00:58:19
- mathxyz
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Re: Property of Function
f(a + b) = f(a) + f(b) ?
Let's try B as an example.
B. F(x) = 5x - 2
F(a) = 5a - 2 F(b) = 5b - 2 F(a+b) = 5(a+b) - 2 = 5a + 5b - 2
So, is F(a) + F(b) equal to F(a+b) ?
Bob
What about h(x) = 2x?
f(a) = 2a
f(b) = 2b
f(a + b) = 2(a + b) =2a + 2b
So, f(a) + f(b) = f(a + b).
1. Am I right?
2. What about g(x)?
3. What about G(x)?
The greatest truth about the Rapture is not its timing but it's reality.
Dr. David Jeremiah
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#4 2024-03-12 01:00:03
- Bob
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Re: Property of Function
Yes h(x) is right.
Try a similar thing with the others.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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#5 2024-03-12 11:49:16
- mathxyz
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- From: Brooklyn, NY
- Registered: 2024-02-24
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Re: Property of Function
Yes h(x) is right.
Try a similar thing with the others.
Bob
Ok. Will do. By the way, after going through the college algebra textbook, I may go straight to calculus l or perhaps try a precalculus textbook. Maybe I should do both courses simultaneously. In fact, I will go through precalculus now along with college algebra.
The greatest truth about the Rapture is not its timing but it's reality.
Dr. David Jeremiah
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