Show that the function f in A = |R - {2/3} defined as f(x) = (4x+3)/(6x-4) is one-one and onto. Hence, find f^{ –1} . ​

Question

Show that the function f in A = |R - {\(\frac{2}{3}\)} defined as f(x) = \(\frac{4x+3}{6x-4}\) is one-one and onto. Hence, find f ^–1 .

Answer 1

One-one : Let x₁,x₂ ∈ A

Hence, f is one-one function.

Onto :

Thus, f is one-one onto function.

Also, f^-1 (x) = \(\frac{4x+3}{6x-4}\)