Function Notation: If f(x) = 2x+1, g(x) = 3-x, find f(a),

[jolie3000]

I'm hoping someone can help me. I haven't done math in 11 years and am jumping back in the pool.
I am working on function notation and have figured most of it out....(i think)...but am confused on a few things.
This is the question i have been working on:

If ƒ(x) = 2x + 1, and g(x) = 3 - x, find:

a) f(a)
b) f(3a)
c) ƒ(x + 1)
d) g(y)
e) g(2x-3)
f) 2ƒ(x)
g) -2g(a)

Now I'm fairly sure I have figured out a-e for example for answer a my work was as follows:

f(a)=2a+1
g(2a+1)=3-(2a+1)
g(2a+1)=3-2a-1
g( f (a)) =2-2a

But I'm lost with f & g????? How do I work with the 2f(x) & the -2g(a)????????

[stapel_eliz]

If ƒ(x) = 2x + 1, and g(x) = 3 - x, find:

a) f(a)
b) f(3a)
c) ƒ(x + 1)
d) g(y)
e) g(2x-3)

To learn how to work with function notation -- in particular, how to evaluate a function at an expression -- try here. For instance:

. . . . .c) f(x + 1) = 2[x + 1] + 1 = 2x + 2 + 1 = 2x + 3

f) 2ƒ(x)
g) -2g(a)

To learn how to do mathematical operations on functions, try here. For instance:

. . . . .example: 2f(x) - 3g(x) = 2(2x + 1) - 3(3 - x) = 4x + 2 - 9 + 3x

...and so forth.

Now I'm fairly sure I have figured out a-e for example for answer a my work was as follows:

f(a)=2a+1
g(2a+1)=3-(2a+1)
g(2a+1)=3-2a-1
g( f (a)) =2-2a

I'm sorry, but I don't see how the above relates to finding f(a)...?

[jolie3000]

thank you for your help, I will definetely do more reading. I really don't know what I'm doing, I have been reading on this site. This was the page that seemed to relate to what they were asking.....I guess not????
http://www.purplemath.com/modules/fcncomp2.htm

[jolie3000]

Hhhmmm, I still don't understand how the 2 in front of the f(x) or the -2 in front of the g(a) ????
Alsois the page I read on Composition of Functions not related to what I'm doing? TIA

[stapel_eliz]

Composition of functions is, as the lesson you read explained, the process of plugging one function into another.

In your case, however, you are doing mathematical operations on functions. The notation may look a bit lairy, but the process is nothing more than what it looks like: If, for instance, they ask you to find "-5*g(x)" (or, which is the same thing, "-5g(x)"), they're asking you to multiply the expression for g(x) by -5, and simplify to get the result they're looking for.

It works in exactly the same way for finding 2*f(x) and -2g(x).

[jolie3000]

ok that makes more sense. However I still don't think I got the answer right, here's what i did for #f
ƒ(2(x))= 2(2(x)+ 1)
ƒ(2(x))= 2(2x+ 1)
ƒ(2(x))= 4x+ 2

[Martingale]

ok that makes more sense. However I still don't think I got the answer right, here's what i did for #f
ƒ(2(x))= 2(2(x)+ 1)
ƒ(2(x))= 2(2x+ 1)
ƒ(2(x))= 4x+ 2

2(2(x)+ 1) is 2f(x)


if

then we treat the as a place holder

so we have



now we put what we want in there

[jolie3000]

Is there a website that gives an explanation and then examples with break downs. I seem to need to see an example from start to finish.
I don't understand how to write it, how to start it
ƒ(x) = 2x + 1, find 2f(x)
Do I? ƒ(2f(x)) = 2(2f(x)) +1

[Martingale]

Is there a website that gives an explanation and then examples with break downs. I seem to need to see an example from start to finish.
I don't understand how to write it, how to start it
ƒ(x) = 2x + 1, find 2f(x)
Do I? ƒ(2f(x)) = 2(2f(x)) +1

suppose we have

then



and

[jolie3000]

ok, ya that's what I was thinking. I think I'm just wrote it weird but I think I had the idea

If ƒ(x) = 2x + 1, Find 2ƒ(x)
I originally worked it out like this:
ƒ(2(x))= 2(2(x)+ 1)
ƒ(2(x))= 2(2x+ 1)
ƒ(2(x))= 4x+ 2
Does this make more sense:
2f(x)=2(2x+1)=4x+2