Find the Inverse of f(x)=3+x2+tan((πx)/2) for -1<x<1: Step-by-Step Guide

[VICKZZA]

Homework Statement

f(x)=3+x2+tan((πx)/2) where -1<x<1...then find f^-1(3)

Homework Equations

y=3+x2+tan((πx)/2)

The Attempt at a Solution

i jave ried to solve first for x and then interchange the x and y,bu i am having problem with the trignometric identity used here...

 

[DeIdeal]

Just making sure:

Is it

f(x) = 3 + x^{2} + \tan{\frac{\pi x}{2}}

you mean?

 

[VICKZZA]

yea...its tan((pi*x)/2)

 

[DeIdeal]

And you're only looking for f^-1(3)? If so, it might be easier to use the definition of an inverse function: What do you know about f(x) if

f^{-1}(3) = x

EDIT: Sorry, made a small-ish error there : P

 

[Ray Vickson]

Homework Statement

f(x)=3+x2+tan((πx)/2) where -1<x<1...then find f^-1(3)

Homework Equations

y=3+x2+tan((πx)/2)

The Attempt at a Solution

i jave ried to solve first for x and then interchange the x and y,bu i am having problem with the trignometric identity used here...

If x2 is supposed to be x², then you need to write it properly. You can either use the "X²" button on the palette at the top of the input panel, or else write the standard text version x^2. Anyway, if f(x) = 3 you need x^2 + tan(pi*x/2) = 0. Can you see what x must be?

RGV

 

[VICKZZA]

yea but can u show me the whole
process

 

[Ray Vickson]

yea but can u show me the whole
process

Who are you responding to? By "u", do you mean "you"? Was your message a question? (It did not end in a question mark!)

If it was a question, I must say that the answer is NO. Read the Forum rules. We are not permitted to do your work for you; we can just give you hints, which has already been done. Now you need to show some of your own work. If you do that and are still stuck you can come back and ask more questions.

RGV