How do I combine functions?

[MathStudent17314]

I am currently working on math homework and I am stuck because I have not been taught on how to combine functions. Thank you in advance!

The question I am stuck on is:

Let f(x) = 8x + 7 and g(x) = 9x − 8.
Find the function.
(f/g)(x) =

Find the domain. (Enter your answer using interval notation.)

 

[tkhunny]

(f/g)(x) = f(x)/g(x) -- It is just a division problem.

 

[MathStudent17314]

(f/g)(x) = f(x)/g(x) -- It is just a division problem.

So would it be 8x+7/9x-8 ?

 

[tkhunny]

So would it be 8x+7/9x-8 ?

Not quite. Remember your order of operations. Try (f/g)(x) = (8x+7)/(9x-8).

 

[pka]

Let f(x) = 8x + 7 and g(x) = 9x − 8.
Find the function.
(f/g)(x) =
Find the domain. (Enter your answer using interval notation.)

So what is \(\left( { - \infty ,\dfrac{8}{9}} \right) \cup \left( {\dfrac{8}{9},\infty } \right)\)?

 

[MathStudent17314]

Not quite. Remember your order of operations. Try (f/g)(x) = (8x+7)/(9x-8).

I was able to figure out the problem, thank you. However I also am having issues with ones like this:

Let f(x) = x^2 − 4 and g(x) = 2x − 3.
Find the value, if possible. (If not possible, enter IMPOSSIBLE.)
(f − g)(−6)

 

[Steven G]

(f-g)(x) = f(x) - g(x)
So (f-g)(-6) = f(-6) - g(-6).

Before you ask: (f+g)(x) = f(x) + g(x) and (f*g)(x) = f(x)*g(x)

All these formulas are in your book.

 

[HallsofIvy]

I was able to figure out the problem, thank you. However I also am having issues with ones like this:

Let f(x) = x^2 − 4 and g(x) = 2x − 3.
Find the value, if possible. (If not possible, enter IMPOSSIBLE.)
(f − g)(−6)

That is possible and there are two ways to do this. The hard way is to say that (f- g)(x)= f(x)- g(x)= x^2- 4- (2x- 3)= x^2- 2x- 1 and then let x= -6.
The easy way is to first calculate f(-6) and g(-6), then subtract those numbers.

Try doing it both ways and see if you get the same answer.

 

[Otis]

8x+7/9x-8

Hello. When texting algebraic fractions, we must enclose numerators and denominators within grouping symbols whenever either contains more than a single number or symbol:

(8x+7)/(9x-8)

It's not a big deal in this thread (because context makes your intent clear), but try to remember going forward because missing grouping symbols will become an issue in future exercises.

8x+7/9x-8 \(\;\) means \(\; 8x + \frac{7}{9x} - 8\)

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