+83 Let f be defined byf(x)={3−x if x≤3,−x3+2x2+3x if x>3.Calculate f−1(0)+f−1(6).
+118704
Consider
y=3−xwherex≤3whenx≤3,y≥0
y=3−xwherex≤3−x=y−3x=3−ythe inverse will bey=3−xwherex≥0
since I only am asked for the inverse values in this domain I do not need to concern myself with the original function when x>3 as this would give an inverse function domain of x<0
To show you, if
f(x)=-x^3+2x^2+3x then
f(3)=-27+18+9 = 0 for values bigger than 3 the value will be negative.
f−1(0)=3−0=3f−1(6)=3−6=−3
Any question? ask away :)
Here is the actual graph
https://www.geogebra.org/classic/nxzepazs
and here is just the pic.
