- #1

mgnymph

- 15

- 0

Question 1

## Homework Statement

Show that, when restricted to the domain [-1,1], g has an inverse function. Use a definition of a theorem, a graph will not be accepted.

## Homework Equations

g(x) = x/(x^2 + 1)

## The Attempt at a Solution

I tried solving this first by going

y = x/(x^2 + 1)

then making x the subject... so..

yx^2 + y = x

yx^2 - x + y = 0

using quadratic formula, i end up with

g^-1(x) = (1+- root(1 - 4x^2) ) / 2x

But I don't get how to prove its an inverse function when x is between -1 and 1.. :(

Question 2...

## Homework Statement

Simplify sin(2tan^-1(x)), tan^-1 is arctan, and state where your simplification is valid.

## The Attempt at a Solution

I made a right angled triangle, with adjacent length 1, opposite length x and hypotenuse length root(1 + x^2).

But I don't know how to deal with that 2...

Thanks (in advance) for helping :D