Find inside function from the given Composite Function

Composite functions are functions of functions. Operations of the inside function are performed and the the outside function. All the operations are performed in an order. Function notation is used to represent output y as g(x) for input x.
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[smg]

I've been crying over this for an hour. Thank you

[abdullahhussain]

For anyone who wants to find the outside function, use the method of finding the inverse.

We know that for example g(x) was the inner function of fg(x), so this means that g(x) was placed inside f(x). To Undo this or reverse this, (get g(x) out and leave us with the f(x) ), we find the inverse of g(x) that was originally placed into it.

Here is an example,

Let’s say that fg(x)= 2x+2 where g(x) is (x+1)

To get f(x) on its own we reverse what has came into it. So we find the inverse of g(x)
Which is x-1

Now we substitute (x-1) into
Fg(x). So instead of fg(x)=2x+2
It’s now f[inverse g(x)]= 2(x-1)+2
Which cancels down to 2x. This is our original f(x).

[AaLl-feix]

1:27 No, it is not cross multiply. It is just a behavior of swapping the denominator with the value of the fraction isn't it?

[hanlydia]

Thank you so much sir!! Awesome teaching. Clearer and more intuitive than any other teaching videos I've seen.

[Koploper]

This helped me a lot, thank you so much!

[gamingtv]

Please help me with this question
If f(x) = 3x +4 and gof = 6x -7÷ 3x +7
Find g(x)

[AaLl-feix]

I actually did pause the video and answered the question, but I can't tell how I did and give the answer because then people who are watching this video might look at this and cheat, and nobody wants that, we want them to learn don't we?


P.S. do you know in which math class we learn this?

[krabzmorningstar]

To make it easier if you need to distribute something to common factor, remember you can let f(x) be some variable!

[arkitbhattacharjee]

Sir if f(x) is given and (gof)(x) is given then how will we do???

[sarazaidalkilani]

you just saved my life my exam is after 27 mins

[J_e_n_tl_e]

Please I need the hard question inside function.

[ashichaudhry]

What will be the value of x for which f( g(x))= Sir solve this
As soon as possible

[pratikshapoudel]

If fg(x) and g(x) is given how to find out f(x)