Inverse function

Question

Find inverse of function g(X)=5^3x+1 -6 and state domain and range. The equation is not divided by 6 but just is -6. The -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 .

Comments

The equation is setup wrong. 3x-1 is the exponent after 5, and the -6 is another number not related to the exponent