3 years ago

If f(x) =7x+5/3-x, then show that fof power -1(x) is an identity function

Mathematics

1 answer:

Irina-Kira [14]3 years ago

4 0

If f(X)= 7x +5/3 - x =6x +5/3

y= 6x +5/3

6x= y-5/3

f^-1(y)=x=(y-5/3)/6

So we can write

f(f^-1(y))= f((y-5/3)/6) = 6 (y-5/3)/6 +5/3= y-5/3+5/3= y

The same result can be obtained for f^-1(f(x))=x

If the function is f(x)= 7x +5/(3-x) then it is not invertible since it is not injective (pictures)

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Read 2 more answers

If f(x) =7x+5/3-x, then show that fof power -1(x) is an identity function ​

If f(x) =7x+5/3-x, then show that fof power -1(x) is an identity function