Certainly! Let's solve the problem step-by-step.
1. Define the functions [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex]:
- [tex]\( f(x) = 5 - x \)[/tex]
- [tex]\( g(x) = x^2 + 3x - 2 \)[/tex]
2. Evaluate [tex]\( f(-1) \)[/tex]:
- Substitute [tex]\( x = -1 \)[/tex] into [tex]\( f(x) = 5 - x \)[/tex]
[tex]\[
f(-1) = 5 - (-1) = 5 + 1 = 6
\][/tex]
3. Evaluate [tex]\( g(-1) \)[/tex]:
- Substitute [tex]\( x = -1 \)[/tex] into [tex]\( g(x) = x^2 + 3x - 2 \)[/tex]
[tex]\[
g(-1) = (-1)^2 + 3(-1) - 2 = 1 - 3 - 2 = 1 - 5 = -4
\][/tex]
4. Calculate [tex]\( \left(\frac{x}{g}\right)(-1) \)[/tex]:
- Substitute [tex]\( x = -1 \)[/tex] and the previously calculated [tex]\( g(-1) \)[/tex]
[tex]\[
\left(\frac{x}{g}\right)(-1) = \frac{-1}{g(-1)} = \frac{-1}{-4} = \frac{1}{4} = 0.25
\][/tex]
5. Combine the results:
- We have found [tex]\( f(-1) = 6 \)[/tex], [tex]\( g(-1) = -4 \)[/tex], and [tex]\( \left(\frac{x}{g}\right)(-1) = 0.25 \)[/tex].
Therefore, the detailed solution yields the results:
- [tex]\( f(-1) = 6 \)[/tex]
- [tex]\( g(-1) = -4 \)[/tex]
- [tex]\( \left(\frac{x}{g}\right)(-1) = 0.25 \)[/tex]
So, the solution to the problem is [tex]\( (6, -4, 0.25) \)[/tex].
