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# C3- Question on functions watch

1. Hi there people I'm stuck on a question. The question is:

A function f is defined by f(x)= 2 - 1/x, x doesn't =0.
Find f⁻¹ and state the value of x for which f⁻¹ is not defined.

I got 2+x as my answer but in the back of the book the answer is given as: f⁻¹(x)= 1 / 2-x, x doesn't = 2

2. Find the inverse. i.e. make x the subject
3. The book's right in this case
x=2-(1/f-1(x))
x-2=-(1/f-1(x))
(f-1(x))(x-2)=-1
f-1(x)=-1/(x-2)
which can be simplified to the answer given
4. take 2 to other side, times both side by 2 than factorise
5. y=2-(1/x)
y+(1/x)=2
xy+1=2x
1=2x-xy
1=x(2-y)
1/(2-y)=x
Then change the y into x
:1/ (2-x) = f⁻¹(x)
The value of x which is not defined is 2, because substituting x=2 into the equation : 1/0 ..Which is undefined.

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Updated: September 25, 2010
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