Let f(x)=1/x-2 and g(x)=1/x+4 ,then what is the domain of (gof)(x) ?

To find the domain of (gof)(x), we need to consider the domains of both f(x) and g(x) and determine the values of x for which the composition is defined.

The domain of f(x) is all real numbers except x = 2, since the function is undefined when the denominator is equal to zero.

The domain of g(x) is all real numbers except x = -4, since the function is undefined when the denominator is equal to zero.

To find the domain of (gof)(x), we need to find the values of x for which g(f(x)) is defined. This means we need to find the values of x for which f(x) is not equal to -4.

f(x) = 1/x - 2
To find the values of x for which f(x) is not equal to -4, we set the denominator equal to zero and solve for x:
x - 2 = 0
x = 2

Therefore, the domain of (gof)(x) is all real numbers except x = 2.