A State the domai and ranga 1 y find the inverse and state t

A. State the domai and ranga. 1. y find the inverse and state the domamamd Tange of f Domain: Rang Graph and sraph.

Solution

f(x) = 3+ 2^x

Domain : ( - inf , inf)

Range : ( 2 , inf )

Inverse : y = 3 +2^x

Plug x= y and y = x:

x = 3 + 2^y

(x -3) = 2^y

take ln on both sides:   ln( x-3 ) = yln2

y = ln2( x-3)

f^-1(x) = ln2( x-3)

Range : ( - inf , inf)

Domain : ( 2 , inf )