Inverse function

Question

Find inverse function g(x)=5^3x+1 -6 and state domain and range. (-6 is not part of the exponent)

Answer 1

Step 1:

The function is .

The function is a linear function with positive slope,hence it is one-to-one function.

Therefore, the inverse of the function exist.

Find the inverse of the function.

Consider and solve in terms of .

Interchange and .

Replace .

Since, Substitute in inverse function then it is represents always negative.

Therefore, the domain of the function is and range is .

Solution:
The inverse of is .

The domain of the function is and range is .