Originally Posted by

**blacktoast94** hi all! i would like to ask a question regarding functions.

let inverse of a function be ' e.g. f '

they always ask u to draw f and f ' on the same graph,

but how about f 'f or ff ' ??

sometimes the f 'f and ff ' functions really become to complicated to form the eqn, cuz usually the power of X goes to 4 or more.

from my understanding, f 'f or ff ' is usually the line of symmetry, is it true? and if so, is it true for both? cuz when i tried to simplify f 'f or ff ' equations, i don't think the end result would be so simple...

and also the questions do not ask u to find f 'f or ff ' eqns before drawing.

please help! thanks so much! .

f ' is normally used for derivative of the graph le....

So you now mean f ' is the inverse of a function.( shuld be written as f^-1)

Anywayz ff^-1 or in ur case ff ' or f 'f shuld be the graph y=x, which is the line of symmetry.(Note: i shall also use f ' as the inverse function)

Why is it y=x? It is based on the definition of the inverse of the function.

Meaning if f(a)=b then f '(b)=a

From f '(b) =a

=> ff '(b)=f(a) =b

So generally, ff '(x)=x. Hence it is y=x graph.

We can also argue the same way for f 'f(x) to get f 'f(x)=x

Also, please do note it is a composite function, so the domain follows the "inner" function.

i.e, domain of ff ' = domain of f '

and domain of f 'f = domain of f

Hope this helps