# Composite function

• Apr 7th 2011, 05:32 PM
jay05
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)
• Apr 7th 2011, 05:38 PM
TheChaz
Quote:

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!
-
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?
• Apr 7th 2011, 05:39 PM
mr fantastic
Quote:

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 ....?
• Apr 7th 2011, 06:19 PM
jay05
Quote:

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?
• Apr 7th 2011, 06:21 PM
TheChaz
Which question are we talking about?
x is not equivalent (or equal) to 1 in either question. Where did you come up with that?
• Apr 7th 2011, 06:24 PM
mr fantastic
Quote:

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?

• Apr 7th 2011, 06:25 PM
jay05
the second question and i just thought that x = 1 like it did in previous algebra problems
• Apr 7th 2011, 06:34 PM
jay05
Quote:

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
• Apr 7th 2011, 06:46 PM
TheChaz
Quote:

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.
• Apr 7th 2011, 09:42 PM
mr fantastic
Quote:

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.