Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Making x the subject of the formula.

g(x)=\frac{x}{x-2}, x \in\mathbb{R}

find

Unparseable latex formula:

g^-^1(x)

I know you have to make x the subject but i can't.

x=g(x-2)

Then I'm stuck.. :s-smilie:

:s-smilie:

:confused:

(edited 11 years ago)

So the function of g is: y=x/(x-2); so you firstly, swap x and y around so you get: x = y/(y-2), then multiply the (y-2) by x to get: x(y-2) = y, then expand the bracket: xy - 2x = y; and move the xy to the other side: -2x = y - xy; then remove the y from the Right hand Side: -2x = y(1-x) and then divide -2x by the bracket: -2x/(1-x) = y

x = y/(y-2)
x(y-2) = y
xy - 2x = y
-2x = y - xy
-2x = y(1-x)
-2x/(1-x) = y

So the inverse of the function is: g^-1(x) = -2x/(1-x)

Also for the person who gave me the negative rating, I believe this function does work and is the exact same as g^-1(x) = 2x/(x-1)

(edited 11 years ago)

g(x) = \frac{x}{x - 2}, x \in\mathbb{R}

g(x)(x - 2) = x

xg(x) - 2g(x) - x = 0

x(g(x) - 1) = 2g(x)

x = \frac{2g(x)}{g(x) - 1}

g^{-1}(x) = \frac{2x}{x - 1}

(edited 11 years ago)

Original post by MrNeilPatel

Also for the person who gave me the negative rating, I believe this function does work and is the exact same as g^-1(x) = 2x/(x-1)

Whilst the neg was not from me

It may well have been because you gave full answer ... that is frowned upon as it is against the forum guidelines

Original post by TenOfThem

Whilst the neg was not from me

It may well have been because you gave full answer ... that is frowned upon as it is against the forum guidelines

Really ? Sorry then; I really didn't know :frown:

:frown:

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