Find the domain , range and inverse of f(x) = ax+b / cx+d where a,b,c,d in mathbb(R) and ad-bc =1

Emmanuel Pace 2022-07-31 Answered
Find the domain , range and inverse of f(x) = ax+b / cx+d where a , b , c , d R and ad-bc =1
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Answers (2)

juicilysv
Answered 2022-08-01 Author has 17 answers
Find the domain , range and inverseof f(x) = ax+b / cx+d where a,b,c,d and ad-bc =1domain is R-{cx+d=0} that is R { d c }
For inverse of y = f ( x ) = a x + b c x + d y c x + y d = a x + b c y x a x = d y + b
x ( c y a ) = d y + b
( c y a ) = d y + b x = d y + b c y a
x = d y + b c y a
f 1 ( x ) = d x + b c x a
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Paxton Hoffman
Answered 2022-08-02 Author has 6 answers
The inverse of the finction is y = d x b a c x . To find this, u replace all of the x's with y's and all of the y's with x's. then u solve for y.
I think that the domain is all real numbers except -d/c and the range is all of the real numbers except f(-d/c)
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