Draw the domain of the following functions Give your answer

Draw the domain of the following functions. Give your answer in interval notation g(x) = e^squareroot 17 + x Domain: __________ g(x) = e^x/(x - 1) Domain: __________ g(x) = x/e^(x + 2) Domain: _____________

Solution

g(x)= e^(sqrt(17+x))

    A square root term is not defined if the value inside the squareroot is negative

So we have to find all the positive values in the square root

17+x>=0

x>=-17

Therefore domain is [-17,infinity)

b) g(x) e^(x/(x-1))

the function is undefined when the bottom of the rational term is zero

x-1=0

x=1

at x =1 the function is undefined

Therefore domain is (-infinity,1)union (1,infinity)

c) g(x)= x/(e^(x+2))

There is no restriction on x

therefore the domain is (-infinity,infinity)