Question

determine the value c that f is continuous

Answer 1

\[f(x)=\] \[x+3;x \le3\]
\[cx+6; x >2\]

Answer 2

i think there is a mistake here

Answer 3

is it maybe
\[f(x) = \left\{\begin{array}{rcc}
x + 3 & \text{if} & x \leq 3 \\
cx+6& \text{if} & x >3
\end{array}
\right.\]

Answer 4

thats it. can you help?

Answer 5

yea, put \(x=3\) and set them equal

Answer 6

you get
\[3+ 3=c\times 3+6\]
\[6=3c+6\]
\[c=0\]

Answer 7

your answer is
\[f(x) = \left\{\begin{array}{rcc}
x + 3 & \text{if} & x \leq 3 \\
6& \text{if} & x >3
\end{array}
\right.\]

Answer 8

I have the answer as c=-1/2

Answer 9

was it maybe this
\[f(x) = \left\{\begin{array}{rcc}
x + 3 & \text{if} & x \leq 2 \\
cx+6& \text{if} & x >2
\end{array}
\right.\]

Answer 10

because \(c=-\frac{1}{2}\) is not right

Answer 11

yes. sorry.

Answer 12

then set
\[2+3=c\times 2+6\]
\[5=2c+6\]
\[2c=-1\]
\[c=-\frac{1}{2}\]

Answer 13

ok that makes sense.

what about for maybe this
f(x)={x+1 if 1<x<3
\[x ^{2} +bx+c\] if \[\left| x-2 \right|\]>1

Answer 14

the answer being b=-3, c=4