To determine [tex]\(f(-1)\)[/tex], [tex]\(f(2)\)[/tex], and [tex]\(f(4)\)[/tex] for the given function [tex]\(f(x)\)[/tex], we can evaluate the function based on the given piecewise definition. Let's go through each value one by one.
1. Finding [tex]\(f(-1)\)[/tex]:
- For [tex]\(x = -1\)[/tex], the function definition states [tex]\(f(x) = \frac{1}{2} x^2 - 5\)[/tex] if [tex]\(x \neq 2\)[/tex].
- Substitute [tex]\(x = -1\)[/tex] into the function:
[tex]\[
f(-1) = \frac{1}{2} (-1)^2 - 5 = \frac{1}{2} \cdot 1 - 5 = 0.5 - 5 = -4.5
\][/tex]
2. Finding [tex]\(f(2)\)[/tex]:
- For [tex]\(x = 2\)[/tex], the function definition directly gives the value:
[tex]\[
f(2) = 3
\][/tex]
3. Finding [tex]\(f(4)\)[/tex]:
- For [tex]\(x = 4\)[/tex], the function definition states [tex]\(f(x) = \frac{1}{2} x^2 - 5\)[/tex] if [tex]\(x \neq 2\)[/tex].
- Substitute [tex]\(x = 4\)[/tex] into the function:
[tex]\[
f(4) = \frac{1}{2} \cdot 4^2 - 5 = \frac{1}{2} \cdot 16 - 5 = 8 - 5 = 3
\][/tex]
So, the values are:
[tex]\[
f(-1) = -4.5
\][/tex]
[tex]\[
f(2) = 3
\][/tex]
[tex]\[
f(4) = 3
\][/tex]
