Thread: how do u do this function composition

if f(x) = x+3 and g(x) = 2x

a) f^ -1 (x)

b) [f * f^ -1](x)

c) [f^ -1 * f](x)

d) g^ -1 (x)

e) [g * g^ -1](x)

f) [g^ -1 * g](x)

Originally Posted by calchelp

if f(x) = x+3 and g(x) = 2x

a) f^ -1 (x)

b) [f * f^ -1](x)

c) [f^ -1 * f](x)

d) g^ -1 (x)

e) [g * g^ -1](x)

f) [g^ -1 * g](x)

does the "*" represent multiplication or a composite function?

That is, when you say [f * f^-1](x), do you mean ? Clarify what you want and we can continue


(a) and (d) are easy though. To get the inverse function, you switch the output and the input and solve for the output. That is, you switch x and y and solve for y.

(a)



For we switch and , so we get:





Therefore,



Now try to find and clarify the other questions. I'm pretty sure you mean though

sorry about that, i dont kno waht other way i could write it out

but yes you were right, i meant




thanks a lot!!!

Originally Posted by calchelp

sorry about that, i dont kno waht other way i could write it out

but yes you were right, i meant




thanks a lot!!!

Ok, i will do (b), the rest are similar.

Recall: and




Note: It will always be the case that if and represent functions that are the inverses of each other, then

Now try the others and show your solutions. All I did was formed the composite function

thanks a lot! i get it now