a) Given: fx=1-x2, 0≤x≤1.
To find : Formula for f-1.
Step 1: Substitute y=f(x), we get
Step 2: Interchange the positions of x and y, we get y=1-x2 . Thus f-1x=1-x2.
Conclusion: Hence f=f-1.
Explanation for graph of f-1: Since f and f-1 are identical, the graphs for f and f-1 are identical about the line y=x (black-coloured graph) and the blue-coloured graph represents f and f-1.