1. ## Composite function

I'm having trouble with these 2 composite function questions

Find the requested composite function value

1.f(x) = 7x + 8, g(x) = -2/x; find (g * f)(3)

2.f(x) = x-6/10, g(x) = 10x + 6; find(g * f)(X)

2. Originally Posted by jay05
I'm having trouble with these 2 composite function questions

Find the requested composite function value

1.f(x) = 7x + 8, g(x) = -2/x; find (g * f)(3)

2.f(x) = x-6/10, g(x) = 10x + 6; find(g * f)(X)
You say "composite functions" but use a standard multiplication symbol (*). Hopefully you mean composition, because that's what follows!
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1. g(f(3)) can be found by first determining f(3), then finding "g of" this value.
f(3) = 7(3) + 8 = 21 + 8 = 29. g(f(3)) = g(29) = -2/29.

2. g(f(x)) = g((x - 6)/10) = ... can you take it from here?

3. Originally Posted by jay05
I'm having trouble with these 2 composite function questions

Find the requested composite function value

1.f(x) = 7x + 8, g(x) = -2/x; find (g * f)(3)

2.f(x) = x-6/10, g(x) = 10x + 6; find(g * f)(X)
What have you tried? Where are you stuck? Do you uderstand the notation (is it explained in your class notes or textbook?) Does * mean you're multiplying the two functions together ....?

4. Originally Posted by TheChaz
You say "composite functions" but use a standard multiplication symbol (*). Hopefully you mean composition, because that's what follows!
-
1. g(f(3)) can be found by first determining f(3), then finding "g of" this value.
f(3) = 7(3) + 8 = 21 + 8 = 29. g(f(3)) = g(29) = -2/29.

2. g(f(x)) = g((x - 6)/10) = ... can you take it from here?
the second x is kind of throwing me off, is x still equivalent to 1?
if so those the equation = 1?

5. Which question are we talking about?
x is not equivalent (or equal) to 1 in either question. Where did you come up with that?

6. Originally Posted by jay05
the second x is kind of throwing me off, is x still equivalent to 1?
if so those the equation = 1?

7. the second question and i just thought that x = 1 like it did in previous algebra problems

8. Originally Posted by mr fantastic
What have you tried? Where are you stuck? Do you uderstand the notation (is it explained in your class notes or textbook?) Does * mean you're multiplying the two functions together ....?
i understand the notation just having trouble with this and no * doesnt mean multiplication i just didnt know what to put in the middle

9. Originally Posted by jay05
the second question and i just thought that x = 1 like it did in previous algebra problems
This is bothering me. In which algebra problems did x = 1?

In question (2), no x-values are specified, so we will end up with g(f(x)) = [some function of x].
You can certainly determine the value of this function WHEN x = 1, but to say that x is equal to 1 is not correct.

10. Originally Posted by jay05
I'm having trouble with these 2 composite function questions

Find the requested composite function value

1.f(x) = 7x + 8, g(x) = -2/x; find (g * f)(3)

2.f(x) = x-6/10, g(x) = 10x + 6; find(g * f)(X)
$\displaystyle g(f(x)) = \frac{-2}{f(x)} = \frac{-2}{7x+8}$. Substsitute x = 3 and get the value.

Alternatively, f(3) = 29. Therefore g(f(3)) = g(29) = -2/29.

Do the other one in the same way.