$$ f(x)=\left\{\begin{array}{ll}x+5 & ext { if } x

Question

$$ f(x)=\left\{\begin{array}{ll}x+5 & 	ext { if } x<1 \ 6 x-12 & 	ext { if } x \geq 1\end{array}ight. $$

UpStudy AI · Accepted Answer

Let's analyze the piecewise function $$ f(x) $$:

$$
f(x) = 
\begin{cases} 
x + 5 & \text{if } x < 1 \ 
6x - 12 & \text{if } x \geq 1 
\end{cases}
$$

To understand this function better, we can evaluate it at specific points, particularly at the boundary $$ x = 1 $$ and a few values on either side of this boundary.

1. **Evaluate $$ f(0) $$** (since $$ 0 < 1 $$):
   $$
   f(0) = 0 + 5 = 5
   $$

2. **Evaluate $$ f(1) $$** (since $$ 1 \geq 1 $$):
   $$
   f(1) = 6(1) - 12 = 6 - 12 = -6
   $$

3. **Evaluate $$ f(2) $$** (since $$ 2 \geq 1 $$):
   $$
   f(2) = 6(2) - 12 = 12 - 12 = 0
   $$

Now we have the following evaluations:
- $$ f(0) = 5 $$
- $$ f(1) = -6 $$
- $$ f(2) = 0 $$

If you need further analysis, such as finding limits, continuity, or specific values, please let me know!
The function $$ f(x) $$ is defined as: - $$ f(x) = x + 5 $$ when $$ x < 1 $$ - $$ f(x) = 6x - 12 $$ when $$ x \geq 1 $$ Evaluations: - $$ f(0) = 5 $$ - $$ f(1) = -6 $$ - $$ f(2) = 0 $$

Solución de inteligencia artificial de Upstudy

Responder

Solución

Extra Insights

preguntas relacionadas

Latest Algebra Questions