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faf3

  • one year ago

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.

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  1. faf3
    • one year ago
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    please help me!

  2. tkhunny
    • one year ago
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    Well, do it. Let's see your best algebra.

  3. faf3
    • one year ago
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    Im not sure what to do.

  4. tkhunny
    • one year ago
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    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.

  5. faf3
    • one year ago
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    I still dont understand. Could you show me step by step how to solve it.

  6. tkhunny
    • one year ago
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    Just did. Your turn. If \(g(x) = \dfrac{x-4}{x+3}\), what is \(g(5)\)?

  7. faf3
    • one year ago
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    would that answer to the question be 2x−5/2(x+1)

  8. tkhunny
    • one year ago
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    You didn't answer my question. What is \(g(5)\)?

  9. faf3
    • one year ago
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    is it the same as saying g(h(x))? just wanted to know before i asnwer

  10. tkhunny
    • one year ago
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    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. \(g(h(x))\;or\;g(5)\).

  11. tkhunny
    • one year ago
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    \(g(5) = \dfrac{5-4}{5+3}\) \(g(h(x)) = \dfrac{h(x)-4}{h(x)+3}\) 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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