Answer:
[tex]g(5) = \frac{2}{3}[/tex]
Step-by-step explanation:
Piecewise function:
A piecewise function has a different rule depending on the input.
In this exercise:
If the input x is equal or less than two, the rule is [tex]|7 - x^2|[/tex], and if it is greater than 2, the rule is:
[tex]\frac{x+1}{2x-1}[/tex]
g(5)
The input is [tex]x = 5 > 2[/tex], so the rule is:
[tex]g(x) = \frac{x + 1}{2x - 1}[/tex]
At [tex]x = 5[/tex]
[tex]g(5) = \frac{5 + 1}{2(5) - 1} = \frac{6}{9} = \frac{2}{3}[/tex]
The answer is [tex]g(5) = \frac{2}{3}[/tex]
