# Answer to Question #20554 in Trigonometry for Kristen Woods

Question #20554

Give the domain of the function.

6a. g(x)=x^3-1

6b. f(t)= 10/(t^2-2t-3)

6c. h(x)= square root of 2x+1

6a. g(x)=x^3-1

6b. f(t)= 10/(t^2-2t-3)

6c. h(x)= square root of 2x+1

Expert's answer

6a. x in (-infinity, +infinity)

6b.find the roots of denominator

t^2-2t-3 = 0

t1=(2+sqrt(4+3*4))/2= 3

t2=(2-sqrt(4+3*4))/2= -1

hence domain is (-infinity, +infinity) except x=3 andx=-1

6c. sqrt(2x+1)

2x+1>0

domain is x>-1/2

6b.find the roots of denominator

t^2-2t-3 = 0

t1=(2+sqrt(4+3*4))/2= 3

t2=(2-sqrt(4+3*4))/2= -1

hence domain is (-infinity, +infinity) except x=3 andx=-1

6c. sqrt(2x+1)

2x+1>0

domain is x>-1/2

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