Question

the doamin of a function g(x) is x>3 and the range is y>1 what are the domain and range of the inverse g^-1(x)

Answer 1

For the inverse function,

The domain is x > 1

The range is y > 3

Explanation:

We have to find the domain and range of the inverse if the domain of g(x) is x > 3 and the range is y > 1.

Now,

Domain of the inverse

Since the domain of the inverse is the same as the range of the original function, the domain is,

(since range of original is y > 1)

The domain is x > 1

Range of the inverse

Since the range of the inverse is the same as the domain of the original so, in our case,

since domain of g(x) is x > 3,

The range is y > 3