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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 )

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A. State the domai and ranga. 1. y find the inverse and state the dom.pdf

  • 1. 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 )