kaylaprincess
  • kaylaprincess
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.
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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kaylaprincess
  • kaylaprincess
So, I know to start from the inside out...
kaylaprincess
  • kaylaprincess
lets have h(x) = 2 ? That's all i know to do at the moment :/
jdoe0001
  • jdoe0001
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?

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jdoe0001
  • jdoe0001
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
jdoe0001
  • jdoe0001
f( h(x) ) really means, you stick h(x) INSIDE f(x), in place of the "x" say \(\bf f(x)=2x+3\qquad h(x)={\color{brown}{ cheese}} \\ \quad \\ f(\ h(x)\ )=2{\color{brown}{ h(x)}}+3\to 2{\color{brown}{ (cheese)}}+3\)
jdoe0001
  • jdoe0001
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
jdoe0001
  • jdoe0001
so.... make up an h(x) function then so we can take it from there
kaylaprincess
  • kaylaprincess
h can be any number ~
jdoe0001
  • jdoe0001
h(x) is an expression, a function

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