Composition of functions

[usawhney]

f(x) = 4x[sup:2gbeprhg]2[/sup:2gbeprhg]-3x+1 and g(x)= _/x-3 find

a) (f o g) (x)
b) (g o f) (8)
c) g<sup>-1[/sup (x)

These ones are hard to get for me i don't know why

Thanks.</sup>

 

[chrisr]

Can you retype g(x) first ?

In any case...

f o g(x) can be written f{g(x)},
or z=g(x)
f o g(x) is f(z).

Replace x with z in f(x) to calculate f(z).

 

[usawhney]

g(x)= square root of x-3

 

[chrisr]

ah!

f o g(x) means f of g(x)

g(x) = sqrt(x-3)

so f o g(x) = f(sqrt[x-3]) = 4{sqrt[x-3]}[sup:2j44yptp]2[/sup:2j44yptp]-3{sqrt[x-3]}+1
=4(x-3) -3sqrt[x-3] +1 = 4x-12-3sqrt(x-3)+1 = 4x-3sqrt(x-3)-11

f o g(x) = 4{g(x)}[sup:2j44yptp]2[/sup:2j44yptp]-3{g(x)}+1

Try applying that logic to the next one, but be sure you can work the first one through.

 

[usawhney]

so...
(g o f)(8)=
=sqrt(8)-3
=2sqrt(2)-3?

how abt c) g[sup:sxhc6307]-1[/sup:sxhc6307]? I don't get that one

 

[chrisr]

hi usawhney,

You may need to practice a little with this example.
Once you can do it right through and it's clear to you,
you've succeeded and you will be able to do other examples successfully.

What is g o f(x) ?

It is g{f(x)}

Say f(x)=c, then g(c) = sqrt(c-3) which is sqrt(4x[supt7uug6c]2[/supt7uug6c]-3x+1-3).

For the inverse function, g(x) = sqrt(x-3) =y
y[supt7uug6c]2[/supt7uug6c]=x-3
x=y[supt7uug6c]2[/supt7uug6c]+3 so g[supt7uug6c]-1[/supt7uug6c](y) = y[supt7uug6c]2[/supt7uug6c]+3 which gives you the value of x that "arrived" at that y, via g(x).

I'm not fully sure that's what you are looking for, however,
because you have an "x" in with the inverse g[supt7uug6c]-1[/supt7uug6c], so can you rewrite that?