Question

Consider the function f(x)=2x^3 +1. Determine whether the inverse of F is a function. Find the inverse.

Answer 1

2.) solve by equating exponents

4^x=(1/2)^x-3

Answer 2

check the graph of x^3+1. No horizontal line crosses it more than once, so its inverse is a function.

4^x = (1/2)^(x-3)
4 = 2^2 = (1/2)^-2, so
(1/2)^(-2x) = (1/2)^(x-3)
-2x = x-3
x = 1