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Sagot :
To solve the problem, follow these steps:
1. Define the functions [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex]:
- [tex]\( f(x) = 3x - 1 \)[/tex]
- [tex]\( g(x) = 2x - 3 \)[/tex]
2. Calculate [tex]\( f(2) \)[/tex]:
[tex]\[ f(2) = 3 \cdot 2 - 1 = 6 - 1 = 5 \][/tex]
3. Evaluate [tex]\( g(x) - f(2) \)[/tex] for each given value of [tex]\( x \)[/tex]:
For [tex]\( x = \frac{3}{2} \)[/tex]:
[tex]\[ g\left(\frac{3}{2}\right) = 2 \cdot \frac{3}{2} - 3 = 3 - 3 = 0 \][/tex]
[tex]\[ g\left(\frac{3}{2}\right) - f(2) = 0 - 5 = -5 \][/tex]
For [tex]\( x = 2 \)[/tex]:
[tex]\[ g(2) = 2 \cdot 2 - 3 = 4 - 3 = 1 \][/tex]
[tex]\[ g(2) - f(2) = 1 - 5 = -4 \][/tex]
For [tex]\( x = \frac{5}{2} \)[/tex]:
[tex]\[ g\left(\frac{5}{2}\right) = 2 \cdot \frac{5}{2} - 3 = 5 - 3 = 2 \][/tex]
[tex]\[ g\left(\frac{5}{2}\right) - f(2) = 2 - 5 = -3 \][/tex]
For [tex]\( x = 4 \)[/tex]:
[tex]\[ g(4) = 2 \cdot 4 - 3 = 8 - 3 = 5 \][/tex]
[tex]\[ g(4) - f(2) = 5 - 5 = 0 \][/tex]
4. Combine the results:
- For [tex]\( x = \frac{3}{2} \)[/tex], [tex]\( g\left(\frac{3}{2}\right) - f(2) = -5 \)[/tex]
- For [tex]\( x = 2 \)[/tex], [tex]\( g(2) - f(2) = -4 \)[/tex]
- For [tex]\( x = \frac{5}{2} \)[/tex], [tex]\( g\left(\frac{5}{2}\right) - f(2) = -3 \)[/tex]
- For [tex]\( x = 4 \)[/tex], [tex]\( g(4) - f(2) = 0 \)[/tex]
So, the result for each value of [tex]\( x \)[/tex] are:
[tex]\[ x = \frac{3}{2} \rightarrow -5 \][/tex]
[tex]\[ x = 2 \rightarrow -4 \][/tex]
[tex]\[ x = \frac{5}{2} \rightarrow -3 \][/tex]
[tex]\[ x = 4 \rightarrow 0 \][/tex]
1. Define the functions [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex]:
- [tex]\( f(x) = 3x - 1 \)[/tex]
- [tex]\( g(x) = 2x - 3 \)[/tex]
2. Calculate [tex]\( f(2) \)[/tex]:
[tex]\[ f(2) = 3 \cdot 2 - 1 = 6 - 1 = 5 \][/tex]
3. Evaluate [tex]\( g(x) - f(2) \)[/tex] for each given value of [tex]\( x \)[/tex]:
For [tex]\( x = \frac{3}{2} \)[/tex]:
[tex]\[ g\left(\frac{3}{2}\right) = 2 \cdot \frac{3}{2} - 3 = 3 - 3 = 0 \][/tex]
[tex]\[ g\left(\frac{3}{2}\right) - f(2) = 0 - 5 = -5 \][/tex]
For [tex]\( x = 2 \)[/tex]:
[tex]\[ g(2) = 2 \cdot 2 - 3 = 4 - 3 = 1 \][/tex]
[tex]\[ g(2) - f(2) = 1 - 5 = -4 \][/tex]
For [tex]\( x = \frac{5}{2} \)[/tex]:
[tex]\[ g\left(\frac{5}{2}\right) = 2 \cdot \frac{5}{2} - 3 = 5 - 3 = 2 \][/tex]
[tex]\[ g\left(\frac{5}{2}\right) - f(2) = 2 - 5 = -3 \][/tex]
For [tex]\( x = 4 \)[/tex]:
[tex]\[ g(4) = 2 \cdot 4 - 3 = 8 - 3 = 5 \][/tex]
[tex]\[ g(4) - f(2) = 5 - 5 = 0 \][/tex]
4. Combine the results:
- For [tex]\( x = \frac{3}{2} \)[/tex], [tex]\( g\left(\frac{3}{2}\right) - f(2) = -5 \)[/tex]
- For [tex]\( x = 2 \)[/tex], [tex]\( g(2) - f(2) = -4 \)[/tex]
- For [tex]\( x = \frac{5}{2} \)[/tex], [tex]\( g\left(\frac{5}{2}\right) - f(2) = -3 \)[/tex]
- For [tex]\( x = 4 \)[/tex], [tex]\( g(4) - f(2) = 0 \)[/tex]
So, the result for each value of [tex]\( x \)[/tex] are:
[tex]\[ x = \frac{3}{2} \rightarrow -5 \][/tex]
[tex]\[ x = 2 \rightarrow -4 \][/tex]
[tex]\[ x = \frac{5}{2} \rightarrow -3 \][/tex]
[tex]\[ x = 4 \rightarrow 0 \][/tex]
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