Q2 of 215 Page 3

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

We have, f (x) = x2 + x + 1 and g(x) = sin x


Now,


fog(x) = f(g(x)) = f(sin x)


⇒ fog(x) = sin2 x + sin x + 1


Again, gof(x) = g(f(x)) = g (x2 + x + 1)


⇒ gof(x) = sin(x2 + x + 1)


Clearly,


fog ≠ gof


More from this chapter

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1

Find fog and gof, if

f(x) = c, c ∈ R, g(x) = sin x2

 1

Find fog and gof, if

f(x) = x2 + 2,

3

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

 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.