Identifying the inverse - Solution

y(t)=10^(log(t)), for 0.1<=t<5.01

y(t)=sin(arcsin(t)) for -1<=t<1.01

y(t)=tan(arctan(t)) for -10<=t<10.01

y(t)=(1/(1/t)) for 0.1<=t<10.01

What do all the above graphs have in common and why?

All the above are graphs of y=t i.e. the identity function.

This is because, in each case, we are taking the composition of a function with its own inverse.

The inverse of a function f is a function that undoes the operation of f. The inverse function is represented by f^-1.

So the composition ff^-1(t)=t is the mapping of t to t.

y=t is called the identity function because it leaves any input value unchanged.

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