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)

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- June 21st 2007, 09:23 PMcalchelphow 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) - June 21st 2007, 09:38 PMJhevon
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 - June 21st 2007, 11:21 PMcalchelp
sorry about that, i dont kno waht other way i could write it out

but yes you were right, i meant

http://www.mathhelpforum.com/math-he...708fbbe5-1.gif

thanks a lot!!! - June 21st 2007, 11:26 PMJhevon
- June 22nd 2007, 11:17 PMcalchelpthanks a lot! i get it now