Question

find the domain and range of each function.
(a)F(x)=(x^2-4)^1/2 (b)G(x)=(x^2+9)^1/2 (c)H(x)=1/x^2 (D)t(x)=cos4x (e)H(G(x))

Answer 1

\[
f(x)=\sqrt{x^2-4}\] you have to make sure that
\[x^2-4\geq 0\] and since
\[x^2-4\] is a parabola facing up it is positive outside the zeros and negative between them so your domain is
\[(-\infty,-2]\cup [2,\infty)\]

Answer 2

range is
\[y\geq 0\] because the radical sign means positive root

Answer 3

\[
g(x)=\sqrt{x^2+9}\] and now
\[x^2+9\geq 9\] for all x, so it is never negative and therefore domain is all real numbers. range is
\[y\geq 0\] for the same reason as the other one

Answer 4

\[H(x)=\frac{1}{x^2}\] domain is all numbers except 0 because you cannot divide by zero. range is
\[y>0\] since a perfect square is always greater than or equal to zero and this is never zero because the numerator is 1

Answer 5

cosine has domain all real numbers. range is
\[[-1,1]\]

Answer 6

THANK YOU!

Answer 7

yw

Answer 8

but how would i do (d) and (e) ?