inverse.py

Created by thabo
Created on February 23, 2024
768 Bytes
f(x)=x^2 -7
+7
y+7=x^2
sqrt
sqrt(y+7)=x
swap
sqrt(x+7)=y
f^-1(x) = sqrt(x+7)
Domain whatever is under the sqrt
must be grather or equal to 0
x+7>_0
-7
x>_-7
if asking for set notai
{xIx>_-7}

f(f^-1(x)) = f(sqrt(x+7))\
now import the original question
where ^2 and -7 come from
= sqrt(x+7))^2 - 7
sqrt and squared cancel ouy
=x+7-7
=X 

Second check
import the og question
F^-1(f^(x))=F^-1(x^2-7)
importing answer
= sqrt(x^2-7)+7
combine first cause its under
Sqrt(x^2)
=X


IF DECIMAL MAKE FRACTION

f(x) = x^3 =9
y-x^3 -9
3sqrt(y +9)= 3sqrt(x^3)
3Sqrt(y+9) = x
swap
3Sqrt(x+9)= y
f^-1(x) = 3sqrt(x+9)

Domain
{xI-infinity<x<+infinity}
f(f^-1(x)) = f(3sqrt(x+9))
insert
=3sqrt(x+9)^3 -9
=x+9-9
=x

f^-1(x^3-9)
Add answer
=3sqrt(x^3-9)+9
=3sqrt(x^3)
=X