Question

determine the range of the function f(x)=(x-3)^2-2

Answer 1

i would start by plugging 0 in for x, what do you get?

Answer 2

is it -2,3 @billj5

Answer 3

@mathmath333

Answer 4

its easy

Answer 5

the answer is -2,3 right @mathmath333

Answer 6

for finding the range u have to find the inverse of function that is

\(\large\ \begin{align} \color{black}{f'(x)\hspace{.33em}\\~\\}\end{align}\)

the domain of
\(\large\ \begin{align} \color{black}{f'(x)\hspace{.33em}\\~\\}\end{align}\)

will be the range of
\(\large \begin{align} \color{black}{f(x)\hspace{.33em}\\~\\}\end{align}\)

here

\(\large \begin{align} \color{black}{f'(x)=3\pm\sqrt{x+2}\hspace{.33em}\\~\\}\end{align}\)

so the
\(\large \begin{align} \color{black}{f'(x)\hspace{.33em}\\~\\}\end{align}\)
will be positive only for
\(\large \begin{align} \color{black}{
x+2>0\hspace{.33em}\\~\\
x>-2\hspace{.33em}\\~\\
}\end{align}\)
hence the range of
\(\large f(x)\)
is
\(\large \begin{align} \color{black}{x|x\in \mathbb{R},x>-2\hspace{.33em}\\~\\
}\end{align}\)

Answer 7

so its -2 and what?

Answer 8

@mathmath333

Answer 9

and all real numbers

Answer 10

thanks so much