Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

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

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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

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

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)?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

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

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

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.