Difference between f(f-inverse) and (f-inverse)f

Some questions on functions require students to understand the difference between  ff-1 and f-1f. Though both = x, they are two different functions because their domains might be different.

Tex2Img_1400150080 while Tex2Img_1400150161

Therefore,

Tex2Img_1400149917 while Tex2Img_1400150309

Example f(x) = x+2, x> 0

Tex2Img_1400150488

Tex2Img_1400150586

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