Certainly! Let's delve into solving the given mathematical expressions step by step.
We are given a function [tex]\( f \)[/tex] with specific values at certain points. The values are:
1. [tex]\( f\left( \frac{-1}{2} \right) = -2 \)[/tex]
2. [tex]\( f(0) = \frac{3}{2} \)[/tex]
3. [tex]\( f(1) = -1 \)[/tex]
4. [tex]\( f(2) = 1 \)[/tex]
5. [tex]\( f(4) = \frac{7}{2} \)[/tex]
Let's go through each one:
1. At [tex]\( x = \frac{-1}{2} \)[/tex]:
[tex]\[
f\left( \frac{-1}{2} \right) = -2
\][/tex]
2. At [tex]\( x = 0 \)[/tex]:
[tex]\[
f(0) = \frac{3}{2}
\][/tex]
3. At [tex]\( x = 1 \)[/tex]:
[tex]\[
f(1) = -1
\][/tex]
4. At [tex]\( x = 2 \)[/tex]:
[tex]\[
f(2) = 1
\][/tex]
5. At [tex]\( x = 4 \)[/tex]:
[tex]\[
f(4) = \frac{7}{2}
\][/tex]
To summarize, the values of [tex]\( f(x) \)[/tex] at the specified points are:
- [tex]\( f\left( \frac{-1}{2} \right) = -2 \)[/tex]
- [tex]\( f(0) = \frac{3}{2} \)[/tex]
- [tex]\( f(1) = -1 \)[/tex]
- [tex]\( f(2) = 1 \)[/tex]
- [tex]\( f(4) = \frac{7}{2} \)[/tex]
Thus, the function [tex]\( f \)[/tex] evaluated at the given points results in:
[tex]\[
\left( -\frac{1}{2}, -2 \right), (0, \frac{3}{2}), (1, -1), (2, 1), (4, \frac{7}{2})
\][/tex]
These are the coordinates of the points that the function [tex]\( f \)[/tex] takes.
