faf3
  • faf3
For the real-valued functions g(x)=(x-4)/(x+3) and h(x)=2x-1, find the composition of g open circle h and specify its domain using interval notation.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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faf3
  • faf3
please help me!
tkhunny
  • tkhunny
Well, do it. Let's see your best algebra.
faf3
  • faf3
Im not sure what to do.

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tkhunny
  • tkhunny
Hint: If f(x) = 2x + 1 And r(x) = 3x - 2 f o r(x) = f(r(x)) = 2x + 1 = 2(r(x)) + 1 = 2(3x-2) + 1 = 6x - 4 + 1 = 6x - 3 We are creating new functions by substituting old ones into other old ones.
faf3
  • faf3
I still dont understand. Could you show me step by step how to solve it.
tkhunny
  • tkhunny
Just did. Your turn. If \(g(x) = \dfrac{x-4}{x+3}\), what is \(g(5)\)?
faf3
  • faf3
would that answer to the question be 2x−5/2(x+1)
tkhunny
  • tkhunny
You didn't answer my question. What is \(g(5)\)?
faf3
  • faf3
is it the same as saying g(h(x))? just wanted to know before i asnwer
tkhunny
  • tkhunny
That's the next question. First, I want to see if you understand the concept of substitution into a function definition. You can answer wither question. \(g(h(x))\;or\;g(5)\).
tkhunny
  • tkhunny
\(g(5) = \dfrac{5-4}{5+3}\) \(g(h(x)) = \dfrac{h(x)-4}{h(x)+3}\) That's ALL I'm looking for. Now, substitute in that last statement the definition for h(x) and do some simplifying.

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