Question

A) g^(-1)(x) = (x + 1)/(4x - 7)

b) g^(-1)(x) = (x - 1)/(4x + 7)
c) g^(-1)(x) = (x - 1)/(4x - 7)
d) g^(-1)(x) = (x + 1)/(4x + 7)

State the domain and range of g in interval notation.
a) Domain: (-[infinity], 7/4) Range: (-[infinity], [infinity])
b) Domain: (-[infinity], 7/4) Range: (-[infinity], 0)
c) Domain: (7/4, [infinity]) Range: (-[infinity], [infinity])
d) Domain: (7/4, [infinity]) Range: (-[infinity], 0)

Answer 1

The domain of g is (7/4, [infinity]) and the range is (-[infinity], [infinity]).

Step-by-step explanation:

The correct answer is (c) Domain: (7/4, [infinity]) Range: (-[infinity], [infinity]).

To find the domain and range of g-1(x), we need to consider the restrictions on the original function g(x).

The given choices for g-1(x) are all of the form (x - 1)/(4x + 7), (x + 1)/(4x - 7), (x - 1)/(4x - 7), and (x + 1)/(4x + 7).

Out of these choices, only option (c) has a domain of (7/4, [infinity]) which means x can take any value greater than 7/4. And the range of option (c) is (-[infinity], [infinity]) which means y can take any real value.