## 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.

1. kaylaprincess

So, I know to start from the inside out...

2. kaylaprincess

lets have h(x) = 2 ? That's all i know to do at the moment :/

3. 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?

4. 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

5. jdoe0001

f( h(x) ) really means, you stick h(x) INSIDE f(x), in place of the "x" say $$\bf f(x)=2x+3\qquad h(x)={\color{brown}{ cheese}} \\ \quad \\ f(\ h(x)\ )=2{\color{brown}{ h(x)}}+3\to 2{\color{brown}{ (cheese)}}+3$$

6. 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

7. jdoe0001

so.... make up an h(x) function then so we can take it from there

8. kaylaprincess

h can be any number ~

9. jdoe0001

h(x) is an expression, a function