Give the domain of each of following functions in interval notation

Question

a) f(x)= sqrt(x2-25)

 

b) g(x)= sqrt(5-x)/x2+x+30)

 

c) h(x) = -3x/sqrt(x)-4

Answer 1

For the square roots, the radicand cannot be negative, or you'll end up with an imaginary number. 

 

So, set the radicand ≥ 0 and solve for the value of the variable, observing all the rules of inequalities.

 

For part b, as an example, you have the sqrt(5-x) in the numerator. Set this: 5-x ≥ 0, therefore, 5 ≥ x.

 

Then, write in interval notation. (-∞,5]. 

 

Check to make sure your denominator will not equal zero at these values.