Consider the functions $f: \mathbb{r}^3 \rightarrow \mathbb{r}$ and $g: \mathbb{r} \rightarrow \mathbb{r}^3$ defined by \[ f(x, y,z) = \left\{ \begin{array}{ll} x+y+z & \ \text{if $xyz=0$} \\ 0 & \ \text{otherwise} \end{array} \right. \hspace{.8in} g(x) = \left\{ \begin{array}{ll} (x,2x, x^2) & \ \text{if $x\neq 0$} \\ (0,0,0) & \ \text{otherwise} \end{array} \right. \] \begin{enumerate} \item check whether $f$ and/or $g$ are injective, surjective, and/or bijective. \item find the compositions $f\circ g$ and $g\circ f$, if/when possible.

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

125 yards

step-by-step explanation:

i take 75 plus 50.

constant of proportionality = 3 and the equation is c = 3p.

step-by-step explanation:

c = kp   where c = amount of caffeine in mg., p = oz of pepsi and k is the constant of proportionality.

substituting the values given:

24 = 8k

k = 3.

the same value of k will be obtained if we substitute the other given values.

if you would like with a question it is easy to get an answer by including some or multi choice options

step-by-step explanation: