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

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
jolie3000
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### Function Notation: If f(x) = 2x+1, g(x) = 3-x, find f(a),

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

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

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

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

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 $f(x)=2x+1$

then we treat the $x$ as a place holder

so we have

$f( )=2( )+1$

now we put what we want in there

$f(x )=2(x )+1$
$f(y )=2(y )+1$
$f( 6x^2+7)=2(6x^2+7 )+1$
$f(\text{crazy} )=2( \text{crazy})+1$
$f(\text{put stuff here} )=2( \text{put stuff here} )+1$

jolie3000
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### Re: Function Notation: If f(x) = 2x+1, g(x) = 3-x, find f(a),

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
Posts: 333
Joined: Mon Mar 30, 2009 1:30 pm
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### Re: Function Notation: If f(x) = 2x+1, g(x) = 3-x, find f(a),

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 $k(x)=x^2+3x+1$

then

$2k(x)=2(x^2+3x+1)=2x^2+6x+2$

and

$k(2x)=(2x)^2+3(2x)+1=4x^2+6x+1$

jolie3000
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Joined: Sat Apr 18, 2009 10:13 pm
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### Re: Function Notation: If f(x) = 2x+1, g(x) = 3-x, find f(a),

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