Question

6) A College Algebra instructor assigned a different function to each of the following students and asked them to determine its domain, using only the given equation (Le. not a graph) Use the idea presented by each student to find the domain of each function. Write your answer in interval notation a) k(x)--1)(+2) b) w(x) -9-x "The stuff under the radical sign has to be 0 or bigger, so Ineed to figure out what values ofx make-9-x bigger than or equal to 0." Iknow I can't divide by 0, so the bottom of the fraction can't be 0." c) g(x) log(3x25) j)3(x-)+5) d) The input of a log has to be positive, so I just need to figure out what makes 3x 5 greater than zero." "IfImultiply this out, I get a quadratic function, and I already know the domain of a quadratic function.

Answer 1

Sowhon kox) = - (9) (x-1) (x+2) except those for Domain = all real values of x which denominator = 0 g (3-1) (x+2) 0 x #1,-2 Domain= 15-20,-2) U (-2,1) 0(2,0) | e w(x) = ✓-9-* Domain = all real values of x value under square root for which the function is greater than 0. -9-x > 0 3 x <-9 Domain = Teo,-9]). NOTE: At x = -9 , value will be o which ů defined function for square root. So, -9 å included in domen.

o gaya log (32"+5) Domain - log function is defined inside log a positive when number 3 382 +5>0 3x2 > -5 - for all values of a since which å postible à å squared. nou n = LAN Domain = |(-.0) and jeu)= 3(++)(2+5) cd Since , thue q no restriction Even I fanction becomes on o, the values of a it å defined. » Domain - [6-00,00) ay
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