SOLUTION: I am trying to find the inverse of each function and express it in the form y=f inverse -1(x). And I need to verify each result by showing that (f composed of f)(x)=f inverse -1 co

Question 84465This question is from textbook algebra for college students
: I am trying to find the inverse of each function and express it in the form y=f inverse -1(x). And I need to verify each result by showing that (f composed of f)(x)=f inverse -1 composed pf f)(x)=I(x). The problem to be solved is:
x = 4y + 1
I get very confused with the composition process and get the functions mixed up. Could you please explain and show step my step process. Thank you. This question is from textbook algebra for college students

Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
I am trying to find the inverse of each function and express it in the form y=f inverse -1(x). And I need to verify each result by showing that (f composed of f)(x)=f inverse -1 composed pf f)(x)=I(x). The problem to be solved is:
x = 4y + 1
GENERALLY WE ARE GIVEN Y=F(X)=SOME FUNCTION OF X SAY Y=F(X)=4X+1...OR..SOME THING LIKE THAT THEN PROCEDURE IS
PUT
1.Y=4X+1
2.SOLVE FOR X
4X=Y-1
X=(Y-1)/4
3.NOW PUT X IN PLACE OF Y ON THE RIGHT SIDE AND THEN WE GET
F INVERSE X =(X-1)/4
TO CHECK
F OF [F INVERSE X] = X
TO SIMPLIFY UNDERSTANDING AND FOR EASE OF WORK
PUT F INVERSE X =Z= (X-1)/4
F[F INVERSE X]=F[Z]= 4Z+1 =[4(X-1)/4]+1 = (4X-4+4)/4 = 4X/4=X
TO CHECK
F INVERSE OF [F(X)]=X
F INVERSE OF[4X+1] .....
TO SIMPLIFY UNDERSTANDING AND FOR EASE OF WORK....
PUT Z=4X+1
F INVERSE OF[Z]=(Z-1)/4 =[4X+1-1]/4=4X/4=X
HOPE YOU UNDERSTOOD
BUT YOU GAVE
X=4Y+1..........LET US FIND F INVERSE Y IN THE SAME MANNER
4Y=X-1
Y=(X-1)/4
HENCE
F INVERSE Y = (Y-1)/4
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