Answer to Question #94029 in Algebra for Joshua

Question

5.Find the domain and range of \\(f(x) = 4 – x^{2})\\, leaving your result in interval notation
a.\\(\\left [ -4,\\infty \\right ],\\left [ -1,\\infty\\)
b.\\(\\left [\\infty, 0 \\right ],\\left [ -1,\\infty\\)
c.\\(\\left [ 4,\\infty \\right ],\\left [ 0,\\infty\\)
d.\\( \\left [ 1,\\infty \\right ],\\left [ 4,\\infty \\)

Answer 1

$f(x)=4-x^2, x \in (-\infin, \infin)$

Let $f(x)=y\\y=4-x^2 \ \ \ \ \ \ \ or,\ \ \ x=\pm\sqrt{4-y}\\$

$x\ will\ be\ real \ if\ (4-y)\ge 0\\or\ \ \ \ y\le 4\\So \ range\ will\ be(-\infty,4]\\\\Domain\ will\ be\ (-\infty,\infty)$