Evaluate the piecewise function:
f(x)= {x^2-25/x-5, if x < -1
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and 2x-3, if x>-1
We are looking or f(4)= and f(-1)= with that whole equation
The one that says "<-1" is suppose to be
"if x less than or equal to -1"
To evaluate the piecewise function, f(x) = { (x^2-25)/(x-5) if x < -1, and 2x-3 if x > -1 }, at the given values of x, you need to substitute the values into the corresponding expressions based on the conditions.
1. Evaluating f(4):
Since 4 is greater than -1, we use the second expression, which is 2x-3:
f(4) = 2(4) - 3
= 8 - 3
= 5
Therefore, f(4) = 5.
2. Evaluating f(-1):
Since -1 is not strictly less than -1, we use the second expression, which is 2x-3:
f(-1) = 2(-1) - 3
= -2 - 3
= -5
Therefore, f(-1) = -5.
By substituting the given values of x into the corresponding expressions, we determine the outputs or evaluations of the piecewise function. Hence, f(4) = 5 and f(-1) = -5.