Q3 of 215 Page 3

If f(x) = |x|, prove that fof = f.

We have, f(x) = |x|


We assume the domain of f = R and range of f = (0,∞)


Range of f ⊂ domain of f


∴ fof exists,


Now,


fof(x) = f(f(x)) = f(|x|) = ||x|| = f(x)


∴ fof = f


Hence proved.


More from this chapter

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1

Find fog and gof, if

f(x) = x2 + 2,

2

Let f(x) = x2 + x + 1 and g(x) = sin x. Show that fog ≠ gof.

 4

If f(x) = 2x + 5 and g(x) = x2 + 1 be two real functions, then describe each of the following functions:

(i) fog


(ii) gof


(iii) fof


(iv) f2


Also, show that fof ≠ f2.

 5

If f(x) = sin x and g(x) = 2x be two real functions, then describe gof and fog. Are these equal functions?