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kaylaprincess

  • one year ago

Here is my function : f(x) = 2x + 3 Walk me through to understand? They ask you to create a new function, h(x). Then assign any number to x. Using complete sentences, explain whether f(h(x)) and h(f(x)) will always result in the same number.

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  1. kaylaprincess
    • one year ago
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    So, I know to start from the inside out...

  2. kaylaprincess
    • one year ago
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    lets have h(x) = 2 ? That's all i know to do at the moment :/

  3. jdoe0001
    • one year ago
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    so.. you can use any arbitrary h(x)? you're not expected to ... use an specific h(x) or there are no instructions on what h(x) is?

  4. jdoe0001
    • one year ago
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    the idea of f( h(x) ) and h( f(x) ) equalling the same value is that, that is TRUE, only when h(x) is the "inverse function" of f(x) and the case is that, when h(x) is the inverse of f(x), then the value for their composite f( h(x) ) is "x", and h( f(x) ) will also yield "x" otherwise, they do not, I assume that's the context

  5. jdoe0001
    • one year ago
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    f( h(x) ) really means, you stick h(x) INSIDE f(x), in place of the "x" say \(\bf f(x)=2x+3\qquad h(x)={\color{brown}{ cheese}} \\ \quad \\ f(\ h(x)\ )=2{\color{brown}{ h(x)}}+3\to 2{\color{brown}{ (cheese)}}+3\)

  6. jdoe0001
    • one year ago
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    now.. h(x) could be, anything if h(x) is ... say \(3x^2+5\) then you replace the "x" for that if h(x) is \(x^3+5x^5\) then you replace "x" for that whatever h(x) is, will be replacing "x", in f(x) that's what f( h(x) ) means

  7. jdoe0001
    • one year ago
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    so.... make up an h(x) function then so we can take it from there

  8. kaylaprincess
    • one year ago
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    h can be any number ~

  9. jdoe0001
    • one year ago
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    h(x) is an expression, a function

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