Question

What is g^-1(x)? What is the domain of g^-1(x)?

Answer 1

Answer:

g⁻¹(x) = 1/x - 4

(-∞, 0)∪(0, ∞)

Step-by-step explanation:

To find g⁻¹(x), switch the places of x and y.  Rearrange the equation so that it is equal to y.

g(x) = 1/(x + 4)

x = 1/(y + 4)

x(y + 4) = (1/(y + 4))(y + 4)

x(y + 4) = 1

(x(y + 4))/x = 1/x

y + 4 = 1/x

y + 4 - 4 = 1/x - 4

y = 1/x - 4

g⁻¹(x) = 1/x - 4

For the domain, you need to look at where x is located in the equation.  For this equation, x is in the denominator by itself.  A fraction cannot have a denominator of 0.  This means that x cannot be equal to 0.  The domain is:

(-∞, 0)∪(0, ∞)