Learning Functions: Help Me Get Started!

[TheOne123]

I have just started to learn function (self learning).

Can someone help me on how to work these out. If someone can get me started I will finish them off.:) Thanks!

$f$: $x$ $\rightarrow$ $x-7$
$g$: $x$ $\rightarrow$ $\frac{1}{x}$
$h$: $x$ $\rightarrow$ $x^2$


Have to work out:

$gh$: $x$ $\rightarrow$
$hg$: $x$ $\rightarrow$
$fh$: $x$ $\rightarrow$
$hf$: $x$ $\rightarrow$
$fgh$: $x$ $\rightarrow$
$f^2$: $x$ $\rightarrow$
$g^2$: $x$ $\rightarrow$
$h^2$: $x$ $\rightarrow$

 

[Ksitov]

I have just started to learn function (self learning).

Can someone help me on how to work these out. If someone can get me started I will finish them off.:) Thanks!

$f$: $x$ $\rightarrow$ $x-7$
$g$: $x$ $\rightarrow$ $\frac{1}{x}$
$h$: $x$ $\rightarrow$ $x^2$


Have to work out:

$gh$: $x$ $\rightarrow$
$hg$: $x$ $\rightarrow$
$fh$: $x$ $\rightarrow$
$hf$: $x$ $\rightarrow$
$fgh$: $x$ $\rightarrow$
$f^2$: $x$ $\rightarrow$
$g^2$: $x$ $\rightarrow$
$h^2$: $x$ $\rightarrow$

Hello !

It's easy, you replace by the functions.

gh = 1/x * x²

gh = x²/x = x

Dont forget to precise where the function is defined.

Bye !

 

[TheOne123]

Thanks! I get it now :)

 

[Ksitov]

Say we what do you find ;) !

 

[HallsofIvy]

Be sure to distinguish between fg(x)= f(x)g(x) and fog(x)= f(g(x)).

 

[Ksitov]

I think here it's: fg = f(x) * g(x)

 

[njama]

I agree with HallsofIvy. I also believe that it is composition.

 

[Ksitov]

But he writes: fg and not f o g.

And he has just start to learn functions.

 

[TheOne123]

It's composites :)

 

[Ksitov]

Oh ! Game Over xD !

g o h = g ( h(x) )

g ( h(x) ) = 1/h(x) = 1/x²

Do you understand?

 

[HallsofIvy]

I agree with HallsofIvy. I also believe that it is composition.

I didn't say that I believed it was composition! I agree with Ksitov that the notation indicates the product of functions. I just wanted to warn about the similarity with composition.

 

[njama]

Ok, sorry, I got book of Discrete Mathematics which states composition like:
fg. It's just matter of notation.