Question

Given that the functions f(x) = 2x - 1 for -1 < x < 4 and g(x) = 4/(x - 2) for 3 < x < 5. What's the domain of the function h(x) = f(x) - g(x)?

(a) 3<x<4 (b) -2<h(x)<5 (c)1<h(x)<5 (d) -2<x<3 (e)NOTA​

Answer 1

hi !!

Explanation:

first the domain of f(x) : 2*-1 -1 < 2x-1 < 2*4 -1 = -3 <2x-1 < 7

now the domain of g(x) : 4/(3-2) < 4/(x-2) < 4/(5-2) = 1.3 < 4/(x-2) < 4

now h(x) = -3 - 1.3 <f(x) - g(x) < 7-4 = - 4.3 < f(x) - g(x) < 3

it is the answer e : None of the Above