# function question

• Jul 10th 2014, 08:12 PM
mathman11
function question
Let R be the set of real numbers.let A=R - {-1/2} and B=R - {2}.let f be a function from A to B defined by f(x)= 4x-3 / 2x+1.

i) Show that f is 1-1
ii) show that f is onto
iii) does f have an inverse? if so find the inverse?

i)f(a)= 4a-3 / 2a+1

f(b) = 4b-3 / 2b+1

4a-3 / 2a+1 = 4b-3 / 2b+1
4a-3(2b+1) = 4b-3(2a+1)
8ab-6b+4a-3 = 8ab-6a+4b-3
-6b = -6a
a=b
hence 1-1

Im having trouble with the onto and inverse part. Can someone assist me please?
• Jul 11th 2014, 01:01 AM
Shakarri
Re: function question
To get the inverse let f(x)=y
$y= \frac{4x-3}{2x+1}$

Rearrange this to get x in terms of y
Then change the variables so that x becomes f(x) and y becomes x
• Jul 11th 2014, 07:54 AM
mathman11
Re: function question
For a function to be invert-able it must be 1-1 and onto .I got that part but how do i do the inverse?
• Jul 11th 2014, 08:38 AM
Shakarri
Re: function question
I just explained how to get the inverse. Try it and if it doesn't work then show us what you tried
• Jul 11th 2014, 08:44 AM
mathman11
Re: function question
Quote:

Originally Posted by Shakarri
I just explained how to get the inverse. Try it and if it doesn't work then show us what you tried

x= y-3 / 2y - 4

f(x) = x-3 / 2x - 4

is this it?