number 10 of the pairs of functions f and g in Exercises 7-12, determine whether

Question

number 10

of the pairs of functions f and g in Exercises 7-12, determine whether well defined; that is, whether the range of g is a subset of the domain o g) (c) erplicitly if it is well defined. Also, determine whether Write (f of f. gof is well defined. Write (go f) () eplicitly if it is well defined. 7. f: Z Z is defined by2 g : N ? Z is defined by g (n) = 2-n. 8, f : N ? R is defined by f (n) = 2-vn g : Z ? Z is defined by g (z) = z+1. 9. f : N ? R is defined by f (n) = log2 (1+1). g N N is defined by g (n) - 2n-1. 10. f : Z ? Z is defined by f (x) = 3x2-2. g : N 2 is defined by g(n) 2- n.

Explanation / Answer

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

Hence, range of g must be subset of domain of F

But, g has range as all integers which is in domain of f hencethis function is valid

f(g(x))=3g(x)^2-2=3(2-x)^2-2=3(4+x^2-4x)-2=3x^2-12x+10

gof(x)=g(f(x))

But, f(0)=-2 which is not in domain of g

Hence, gof is not defined

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