f(g(x))=(7x+4)/(-19x-4); g(x) = (2-x)/(5x+4). Find f(x).

Question

anonymous · Answer

do u know the properties of inverse function?

anonymous · Answer

like this
$$g(g^{-1}(x))=x$$

anonymous · Answer

@average_student

anonymous · Answer

yes! is that applicable in getting the f(x)?

anonymous · Answer

yes
compute $$g^{-1}(x)$$
then put it in the f(g(x)) equation u will have
$$f(g(g^{-1}(x)))=f(x)=\frac{7g^{-1}(x)+4}{-19g^{-1}(x)-4}$$

anonymous · Answer

it's wrong when i did the checking :(

anonymous · Answer

maybe im wrong!
@dpaInc

anonymous · Answer

could u plz give us the the answer to chech it
tnx

anonymous · Answer

f(x) = (3x+2)/(4x-3)

anonymous · Answer

i need the solution :((

anonymous · Answer

:(((

anonymous · Answer

what do u think dpaInc ? am i right?

anonymous · Answer

@amistre64 
plz check this

amistre64 · Answer

hmmm, this is an undoing is it ....

amistre64 · Answer

i like your inverse concept

amistre64 · Answer

$$y=\frac{2-x}{5x+4}$$
$$x=\frac{2-y}{5y+4}$$
$$x(5y+4)=2-y$$
$$5xy+4x=2-y$$
$$5xy+y+4x-2=0$$
$$y(5x+1)+4x-2=0$$
$$y=\frac{2-4x}{5x+1}$$

$$g^{-1}(x)=\frac{2-4x}{5x+1}$$

amistre64 · Answer

$$f(g(g'(x)))=f(x)=\frac{7(2-4x)+4}{-19(5x+1)-4}$$

amistre64 · Answer

of course we would want to make sure the domain is fair game, but thats usually a sidenote

anonymous · Answer

tnx

amistre64 · Answer

and i see i mixed up the g' lol :)  i put half up top and half underneath