Question

Determine whether the function has an inverse function. f(x)= 3x+4​ / 4x+5 Yes, f does have an inverse. No, f does not have an inverse. If it does, then find the inverse function. (If an answer does not exist, enter DNE.) f −1 (x)=

Answer 1

Hi,

Explanation:

`\\x\\eq (-5)/(4) \\\\f(x)=y=(3x+4)/(4x+5) \\\\Exchanging\ x\ and\ y\\x=(3y+4)/(4y+5) \\\\Solving\ for \ y\\(4y+5)*x=3y+4\\4xy+5x=3y+4\\4xy-3y=4-5x\\y(4x-3)=4-5x\\\\y=(4-5x)/(4x-3) \ if\ x\\eq (3)/(4) \\`

Yes, f has an inverse function (x≠0.75)

`\boxed{f^(-1)(x)=(4-5x)/(4x-3) }`