Answer :
To find [tex]\( f(-4) \)[/tex] for the given piecewise function, we need to determine which part of the function to use based on the value of [tex]\( x = -4 \)[/tex].
The function is defined as:
[tex]\[
f(x)=\left\{\begin{array}{ll}
3x^2 + 1 & \text{for } x < 0 \\
x^2 - 3x & \text{for } x \geq 0
\end{array}\right.
\][/tex]
Since [tex]\( -4 \)[/tex] is less than 0, we will use the first part of the function, which is [tex]\( 3x^2 + 1 \)[/tex].
Let's substitute [tex]\( x = -4 \)[/tex] into the expression:
1. Substitute [tex]\(-4\)[/tex] into the expression [tex]\(3x^2 + 1\)[/tex]:
[tex]\[
3(-4)^2 + 1
\][/tex]
2. Calculate [tex]\((-4)^2\)[/tex]:
[tex]\[
(-4)^2 = 16
\][/tex]
3. Multiply 16 by 3:
[tex]\[
3 \times 16 = 48
\][/tex]
4. Add 1 to the result:
[tex]\[
48 + 1 = 49
\][/tex]
Thus, the value of [tex]\( f(-4) \)[/tex] is 49.
The function is defined as:
[tex]\[
f(x)=\left\{\begin{array}{ll}
3x^2 + 1 & \text{for } x < 0 \\
x^2 - 3x & \text{for } x \geq 0
\end{array}\right.
\][/tex]
Since [tex]\( -4 \)[/tex] is less than 0, we will use the first part of the function, which is [tex]\( 3x^2 + 1 \)[/tex].
Let's substitute [tex]\( x = -4 \)[/tex] into the expression:
1. Substitute [tex]\(-4\)[/tex] into the expression [tex]\(3x^2 + 1\)[/tex]:
[tex]\[
3(-4)^2 + 1
\][/tex]
2. Calculate [tex]\((-4)^2\)[/tex]:
[tex]\[
(-4)^2 = 16
\][/tex]
3. Multiply 16 by 3:
[tex]\[
3 \times 16 = 48
\][/tex]
4. Add 1 to the result:
[tex]\[
48 + 1 = 49
\][/tex]
Thus, the value of [tex]\( f(-4) \)[/tex] is 49.
