Gate Discrete Mathematics

Question

If f : R - > R defined by  , Show that f is invertible.

Answer 1

y= f(x) = 7 - 2x /3

which gives 

x = 7 - 3y / 2

Now , take x = g(y) = 7 - 3y / 2

Hence, we find now

g( f( x ) ) = 7 - 3 (7 - 2x / 3)/2 = x

and

f( g( y )) = 7 - 2 ( 7 - 3y / 2)/3 = y

Now, since

g( f( x ) ) = x and f( g( y ))  = y both are overlapping st. lines

Hence, f(x) is invertible and f ^-1 = g = 7 - 3x / 2 .

Comments

you should have proved....function...first as surjection & injection...then...you can say itz invertible...

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@kapil. Tauhin is right. You should prove that f(x) is one-to-one correspondence i.e. 1-1 and onto. Only then the function is invertible. You have taken x from y and again put it in the same eqn. Thats not correct.