Q17 of 73 Page 84

Let f : R → R : f(x) =x2 and g : C → C: g(x) =x2, where C is the set of all complex numbers. Show that f ≠ g.

It is given that f : R → R and g : C → C

Thus, Domain (f) = R and Domain (g) = C


We know that, Real numbers ≠ Complex Number


∵, Domain (f) ≠ Domain (g)


∴ f(x) and g(x) are not equal functions


∴ f ≠ g


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15

Let R+ be the set of all positive real numbers. Let f : R+→ R : f(x) = logex. Find

(i) range (f)


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Let f : R → R : f(x) =2x. Find

(i) range (f)


(ii) {x : f(x) = 1}.


(iii) Find out whether f(x + y) = f(x). f(y) for all x, y ϵ R.


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f, g and h are three functions defined from R to R as following:

(i) f(x) = x2


(ii) g(x) = x2 + 1


(iii) h(x) = sin x


That, find the range of each function.


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Let f : R → R : f(x) = x2 + 1. Find

(i) f–1 {10}


(ii) f–1 {–3}.