QuestionFind $f(-3)$ for the piecewise function $f(x)=\begin{cases}8 x+1 & \text{if } x<3 \\ 3 x & \text{if } 3 \leq x \leq 5 \\ 3-3 x & \text{if } x>5\end{cases}$ .

Studdy Solution

STEP 1

Assumptions1. The function $f(x)$ is defined as a piecewise function with three different expressions for different ranges of $x$ . . We need to find the value of $f(-3)$ .

STEP 2

First, we need to determine which expression to use for $f(-)$ . We do this by looking at the conditions for each expression in the piecewise function.
The conditions are1. $8x +1$ if $x <$
2. $x$ if $\leq x \leq5$ . $-x$ if $x >5$
Since $-$ is less than $$, we use the first expression $8x +1$.

STEP 3

Now, we substitute $-3$ into the first expression to find $f(-3)$ .
$f(-3) =8(-3) +1$

STEP 4

Calculate the value of $f(-3)$ .
$f(-3) =8(-3) +1 = -24 +1 = -23$ So, $f(-3) = -23$ .

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