how to get the domain of composition of functions? or just steps...

Question

amistre64 · Answer

compositions are somewhat complicated

the domain of the input function is altered so that the range of the function falls within the domain of the other function.

then the range of the other function is adjusted to fit the inputs

anonymous · Answer

the domain of the compostion will be all of the input values of the inside function that leads to outputs of the inside function which are in the domain of the outside function.

czarluc · Answer

like what is the domainof this?
Given f(x) = 3x2 + 2x − 1 and g(x) = 4x + 2, find [f º g](x)?
f(4x + 2)

             = 3(4x + 2)2 + 2(4x + 2) − 1

             = 3(16x2 + 16x + 4) + 8x + 4 − 1

             = 48x2 + 56x + 15

amistre64 · Answer

refresh clears the odd markers

anonymous · Answer

f, g...

$$\left( f \circ g \right)\left( x \right)  = f \left( g \left( x \right) \right)$$

f is the outside functiona nd g is the inside function

czarluc · Answer

that's minus one sorry

anonymous · Answer

what's the domain of f?

amistre64 · Answer

your f and g have no bad maths, and their composition causes no bad maths ... so the domain will remain the same

czarluc · Answer

it's R

anonymous · Answer

$\mathbb{R}$

czarluc · Answer

oh so just get the intersection of both?

amistre64 · Answer

nothing in g makes f go bad ... so the domain of  f(g) is the same as the domain of g

anonymous · Answer

and what's the domain and range of g?

czarluc · Answer

thanks for the reply guys...
pg, it's d= R and R= R

amistre64 · Answer

since pg is sounding more technical to me, and adequate as well, ill defer this to him :)