#### Howdoyoumath

##### New member
Given that f(x)=(x−3)^2 and g(x)=7−2x find

(a) (f+g)(3)=

(b) (f−g)(3)=

(c) (fg)(3)=

(d) (f/g)(3)=

Thanks

#### Otis

##### Senior Member
Hello. What kind of help do you need? That is, where did you get stuck?

Are you able to calculate the value of f(3) and the value of g(3) separately? If so, then add those two numbers (for part a). If you don't understand the symbols f(3) and g(3) -- or how to find their values -- please let us know.

(f+g)(3) means f(3) + g(3)

Likewise, (f−g)(3) means f(3) - g(3)

(fg)(3) = f(3) ∙ g(3)

(f/g)(3) = f(3) / g(3)

If you've started, please show the work you've tried so far.

PS: Check out the Read Before Posting notice, too. Thanks!

#### Jomo

##### Elite Member
Given that f(x)=(x−3)^2 and g(x)=7−2x find

(a) (f+g)(3)=

(b) (f−g)(3)=

(c) (fg)(3)=

(d) (f/g)(3)=

Thanks
f(x) says to subtract 3 from x and then square the result. So f(3) says to subtract 3 from 3 and then square the result.
g(x) says to subtract twice x from 7. So g(3) says to subtract twice 3 from 7, that is 7-6.

#### Howdoyoumath

##### New member
Hello. What kind of help do you need? That is, where did you get stuck?

Are you able to calculate the value of f(3) and the value of g(3) separately? If so, then add those two numbers (for part a). If you don't understand the symbols f(3) and g(3) -- or how to find their values -- please let us know.

(f+g)(3) means f(3) + g(3)

Likewise, (f−g)(3) means f(3) - g(3)

(fg)(3) = f(3) ∙ g(3)

(f/g)(3) = f(3) / g(3)

If you've started, please show the work you've tried so far.

PS: Check out the Read Before Posting notice, too. Thanks!

I have absolutely no idea about how i would start to answer this question. I'm guessing I need to graph the f(x)=(x−3)^2 and g(x)=7−2x into my calculator to determine the x values for each. For f(x)=(x−3)^2 the x value would be f(3)=(3−3)^2. Which doesn't make any sense because that would make it 0. Now if 0 is the correct answer do I plug that 0 for f into the given solutions like
(a) (f+g)(3)=

(b) (f−g)(3)=

(c) (fg)(3)=

(d) (f/g)(3)= ???
If so I think i have an idea on how to finish the problem.

#### pka

##### Elite Member
Suppose that $$\displaystyle f~\&~g$$ are real valued functions with the same domain. Then
$$\displaystyle (f\pm g)(x)=f(x)\pm g(x)$$
$$\displaystyle \dfrac{f}{g}(x)=\dfrac{f(x)}{g(x)}$$

#### Harry_the_cat

##### Senior Member
Given that f(x)=(x−3)^2 and g(x)=7−2x find

(a) (f+g)(3)=

(b) (f−g)(3)=

(c) (fg)(3)=

(d) (f/g)(3)=

Thanks
From post #4 it is clear that you don't understand function notation.
If $$\displaystyle f(x) = (x - 3)^2$$ then

$$\displaystyle f(1) = (1 - 3)^2 = (-2)^2 = 4$$
$$\displaystyle f(2) = (2 - 3)^2 = (-1)^2 = 1$$

So.… $$\displaystyle f(3) = ...….$$

In $$\displaystyle f(x) = (x-3)^2$$, "f" is the name of the function (subtract 3 and then square) and x is the variable used in the function. x can take any value and f(x) is calculated accordingly.
$$\displaystyle g(x)=7 - 2x$$ is a different function (double the number and then subtract from 7) and so has a different name "g".
So $$\displaystyle g(1) = 7 - 2*1 = 5$$ etc.

Now what is f(3) and g(3)? (No graphing is needed)

You have been told above that (f+g)(x) = f(x) + g(x), so (f+g)(3) = f(3) + g(3) = ...... + ...... = ..........

Now do a similar thing with the other 3 questions.

#### Harry_the_cat

##### Senior Member
I have absolutely no idea about how i would start to answer this question. I'm guessing I need to graph the f(x)=(x−3)^2 and g(x)=7−2x into my calculator to determine the x values for each. For f(x)=(x−3)^2 the x value would be f(3)=(3−3)^2. Which doesn't make any sense because that would make it 0. Yes it is 0 ...why doesn't that make any sense? 0 is a number just like any other number
Now if 0 is the correct answer do I plug that 0 for f into the given solutions like You don't plug 0 for f, you plug 0 for f(3) because f(3) =0
(a) (f+g)(3)= f(3) + g(3) = 0 + ……. you finish it now

(b) (f−g)(3)=

(c) (fg)(3)=

(d) (f/g)(3)= ???
If so I think i have an idea on how to finish the problem.
See red above

#### Jomo

##### Elite Member
You need to know how to calculate the functions f and g in words. I stated the rules above in my previous post. Read it, think about, read it again repeat until you understand it.

#### HallsofIvy

##### Elite Member
For f(x)=(x−3)^2 the x value would be f(3)=(3−3)^2. Which doesn't make any sense because that would make it 0. Now if 0 is the correct answer do I plug that 0 for f into the given solutions
Yes, f(3)= 0. Why would that not make any sense? Surely you have seen many functions that have a value for some x? Yes, you "plug" that 0 into the given formulas. What did you get for g(3)?

(Your grammar is a little odd. It is not the "x value" that would be 0. The f value is 0 when the x value is 3. And you do not "plug that 0 for f into the given solutions" because there are NO "given solutions! You plug f(3)= 0 into the given formulas in order to get your solutions.)

#### Jomo

##### Elite Member
f(x)=(x−3)^2 and g(x)=7−2x
(f+g)(3) = f(3) + g(3) = [(3-3)^2] + [7-2*3] = [0] + [1] = 1