If f(x)=(3x-4)/(5x-3); find f^(-1) .
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Step-by-step explanation:
Given:-
f(x)=(3x-4)/(5x-3)
To find:-
Find f^(-1) ?
Solution:-
Given equation is f(x)=(3x-4)/(5x-3)
Let y = f(x)
=>x => f^-1(y)
=>y = (3x-4)/(5x-3)
=>y(5x-3) = 3x-4
=>5xy -3y = 3x -4
=>5xy -3y -3x = -4
=>(5xy-3x)-3y = -4
=>x(5y-3)-3y = -4
=>x(5y-3) = 3y-4
=>x = (3y-4)/(5y-3)
=>f^-1(y) = (3y-4)/(5y-3)
Now, f^-1(x) = (3x-4)/(5x-3)
=>f^-1(x)=y
Now put x = 1 then
=>f^-1(1) = (3(1)-4)/(5(1)-3)
=>(3-4)/(5-3)
=>-1/2
and
Put x = -1 then
f^(-1) = (3(-1)-4)/(5(-1)-3)
=>(-3-4)/(-5-3)
=>-7/-8
=>7/8
Answer:-
f^-1(x) = (3x-4)/(5x-3)
f^-1(1) = -1/2
f^(-1) = 7/8 for the given problem
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