Hey there! Sign in to join this conversationNew here? Join for free
x Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    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

    so please hlep guys. Thanks
    Offline

    14
    ReputationRep:
    Find the inverse. i.e. make x the subject
    Offline

    2
    ReputationRep:
    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
    Offline

    2
    ReputationRep:
    take 2 to other side, times both side by 2 than factorise
    Offline

    3
    ReputationRep:
    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.
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: September 25, 2010
Poll
Do you agree with the proposed ban on plastic straws and cotton buds?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.