Question

I also need help with : express the domain of the given function using interval notation

click on this and it will show the rest!!! please help!

Answer 1

\[f(x)=\sqrt{8-8x^{2}}\]

Answer 2

the condition for which you must solve is\[8-8x^2 \ge0\]divide through by 8\[1-x^2 \ge0\]factor difference of two squares to find roots\[(1-x)(1+x) \ge0\]since there is a negative in front of the squared term the x-values are positive between the two roots -1 and 1, thus, the domain is

[-1, 1]

Answer 3

a rough sketch of the radicand as function is the procedure I used; attached is a sketch where you can see the graph is positive between the roots -1 and 1

Answer 4

thank you so much!!! do you mind helping me on my other one!?

Answer 5

ok

Answer 6

I need help with : Express the domain of the given function using interval notation.\[f(x)=\sqrt{2x ^{2}-8}\]

Answer 7

set the radicand GE 0 and solve for x\[2x^2-8 \ge 0\]divide by 2\[x^2-4 \ge 0\]find the roots\[(x-2)(x+2) \ge0\]the roots are x=-2 or x=2. since the lead coefficient is positive, the parabola opens upward and positive to the left of -2 and positive to the right of 2, or the domain is\[(- \infty, -2] \cup [2, \infty)\]again the rough sketch shows the parabola to be positive outside the roots:

Answer 8

Thank you sooo much!!!!

Answer 9

np:})