Question

Is the function given by, (Picture Provided)

Answer 1

a. yes

Explanation:

The given function is

`f(x)=\left \{ {{3x-2,if\:x\le3} \atop {10-x,if\:x\:>\:3}} \right.`

`f(3)=\left \{ {{3(3)-2,if\:x\le3} \atop {10-3,if\:x\:>\:3}} \right.=7`

`\lim_(x \to 3^-) f(x)=3(3)-2=7`

`\lim_(x \to 3^+) f(x)=10-3=7`

`\Rightarrow \lim_(x \to 3) f(x)=7`

Since;

`\lim_(x \to 3) f(x)=f(3)`

The function is continuous at
`x=3`