if the function is defined by f(x)=(ax-2)/(2x-3), x is not equal to k, satisfies f(x)=x for all real values of x except k
(i) State the value of k
(ii) State the range of values of a

(i)f(x)=(ax-2)/(2x-3)
ax-2/2x-3=x
x(2x-3)=ax-2
x(2x-3-a)=-2
2=x(a+3-2x)

Question

if the function is defined by f(x)=(ax-2)/(2x-3), x is not equal to k, satisfies f(x)=x for all real values of x except k 
(i) State the value of k 
(ii) State the range of values of a

(i)f(x)=(ax-2)/(2x-3)
ax-2/2x-3=x
x(2x-3)=ax-2
x(2x-3-a)=-2
2=x(a+3-2x)

anonymous · Answer

Well then, if i'm reading you right$$2x-3=0\rightarrow x=3/2\rightarrow k= 3/2$$And then,$$x=(ax-2)/(2x-3)\rightarrow x(2x-3)=ax-2 \rightarrow ax = 2x ^{2}-3x+2$$So... a can be equal to pretty much anything.

Hope i could help, didn't really got your question.
Cheers.