Question

1. Determine the inverse of y=2(3)^x+1

2. convert 1600 degree to radian measure, in term of x radian.

Answer 1

`f(x)=2\cdot3^x+1\\ y=2\cdot3^x+1\\ 2\cdot 3^x=y-1\\ 3^x=(y-1)/(2)\\ x=\log_3(y-1)/(2)\\ f^(-1)(x)=\log_3(x-1)/(2)\\`


`\alpha_{\text{rad}}=\alpha_{\text{deg}}\cdot(\pi)/(180)\\ \alpha_{\text{rad}}=1600\cdot(\pi)/(180)\\ \alpha_{\text{rad}}=(80)/(9)\pi\approx27.9`