Question d801a

Oct 1, 2016

$- 3$ is the correct option.

Explanation:

A Function of $x$ means there is a "rule" (or process) which uses values of x and after some calculation, gives a y value.
$f \left(x\right) = y$

$\textcolor{m a \ge n t a}{x - - - - \rightarrow}$ (some process) $\textcolor{m a \ge n t a}{- - - \rightarrow y}$

The process is given as the expression in the function.

So, for $f \left(\textcolor{red}{x}\right) = \textcolor{red}{x} - 2$ we can find $f \left(4\right)$ by substituting 4 for $x$

$f \left(\textcolor{red}{4}\right) = \textcolor{red}{4} - 2 = 2 \rightarrow$ This gives $\left(x , y\right) \text{ as } \left(4 , 2\right)$

Using different x-values will give a whole set of points.
The set of points is the function, which can also be graphed.

$g \left(x\right)$ just means different "rule" or equation is used to find a y-value for any x-value that is used.

We have two functions. $f \left(x\right) \text{ and } g \left(x\right)$

$f \left(x\right) = x - 2 \text{ and } g \left(x\right) = {x}^{2} - 7 x - 9$

Find $\textcolor{red}{f} \left(\textcolor{b l u e}{g \left(- 1\right)}\right)$ means:

First use -1 for $x$ in the 'g' rule, then use THAT value in the 'f' rule.

$\textcolor{m a \ge n t a}{x - - - - \rightarrow}$ (some process) $\textcolor{m a \ge n t a}{- - - \rightarrow y}$

color(magenta)((-1) ----rarr (x^2 -7x-9) color(magenta)( ---rarr y)#

$\textcolor{b l u e}{g \left(- 1\right)} \text{ simply means use -1 for every "color(blue)(x)" in } {\textcolor{b l u e}{x}}^{2} - 7 \textcolor{b l u e}{x} - 9$

$g \left(- 1\right) = {\left(- 1\right)}^{2} - 7 \left(- 1\right) - 9$
$= 1 + 7 - 9$
$= \textcolor{red}{- 1}$

Now find $\textcolor{red}{f \left(- 1\right)}$
$f \left(\textcolor{red}{- 1}\right) = \textcolor{red}{- 1} - 2 = - 3$