Question

Find the domain of the radical function.
f(x)=√2-3(x+1)

Answer 1

Radical functions are undefined for any value of x that causes the radicand to be less than zero. So the domain of \[f(x)=\sqrt{2-3(x+1)}\] Will be all values of x except those that cause the radicand to be less than zero. So we need to examine the inequality \[2-3(x+1)<0\] Distributing the -3 we get\[-3x-1<0\] You can add 1 to both sides and divide by -3 to solve for x. Because we divided by a negative, we have to flip the inequality sign.\[x>-1/3\] So the domain of the function will any real number than is less than or equal to -1/3 because the function is undefined for any value greater then -1/3. In set builder notation the domain is\[\left\{ x:x \le-1/3 \right\}\] In interval notation it would be \[(-\infty,-1/3]\]

Answer 2

wow! thank you!

Answer 3

My pleasure =)