Question

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.

Answer 1

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

Answer 2

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

Answer 3

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?

Answer 4

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

Answer 5

f( h(x) )

really means, you stick h(x) INSIDE f(x), in place of the "x"

say \(\bf f(x)=2x+3\qquad h(x)={\color{brown}{ cheese}}
\\ \quad \\
f(\ h(x)\ )=2{\color{brown}{ h(x)}}+3\to 2{\color{brown}{ (cheese)}}+3\)

Answer 6

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

Answer 7

so.... make up an h(x) function then

so we can take it from there

Answer 8

h can be any number ~

Answer 9

h(x) is an expression, a function