(7).Given f(x) =
and g(x)=
where x & R.

Find the ;
(i). inverse of g(x) (ii). Expression

iii). Largest domain of f(x) and g(x) respectively.​

The inverse of g(x) is

The domain of g(x) is (-∞,-2)U(-2,∞)

The domain of f(x) is (-∞,-1)U(-1,1)U(1,∞)

Step-by-step explanation:

Find the inverse of g(x).

Solve for x

Find the domain of g(x)

Numerator and denominator have domain

(-∞,∞).

However, g(x) is undefined if the denominator is 0.  Hence, x=-2 must be taken out of the domain. So, the domain of g(x) is

(-∞,-2)U(-2,∞).

Find the domain of f(x)

The numerator and denominator have the domain

(-∞,∞)

However, f(x) is undefined if the denominator is 0.  This rules out +1 and -1. So, the domain of f(x) is

(-∞,-1)U(-1,1)U(1,∞)

I am not sure what you mean for (ii).

you need to show us the graph.

step-by-step explanation: