For the given functions find f composition gx and g composit

For the given functions, find (f composition g)(x) and (g composition f)(x) and the domain of each. F(x) = 8/1 - 5x, g(x) = 1/x What is the domain of f composition g? (-infinity, 0)union (0, 5) union (5, infinity) (-infinity, 5) union (5, infinity) (-infinity, -5)union (-5, 0) union (0, infinity) (-infinity, 0) union (0, infinity) What is the domain of g composition f? (-infinity, 1/5)union(1/5, infinity) (-infinity, 5)union(5, infinity) 9-infinity, 0)union(0, infinity) (-infinity, 0)union(0, 1/5)union(1/5, infinity)

Solution

Dear Student

Thank you for using Chegg !!

Given f(x) = 8 / (1- 5x )

g(x) = 1/x

a) fOg(x) = 8 / (1-5(1/x))

= 8x / (x - 5)

b) gof(x) = 1 / [8/(1-5x)]

= (1-5x) / 8

c) Option A since when x = 5, Denominator will become 0, Fraction cannot be be defined with 0 denominator.

And at x =0 , g(x) is not defined

d) Option A, Since gof is defined every where but f(x) is not defined at x = 1/5.

Solution