Question

Составить алгоритм и программу вычисления функции f(x) при произвольном x:f(x)={(2x+4,если-2≤x≤-1;2x^2,если-1<x≤1;-2x+2,если 1<x≤2;)При x < -2 и x >2 функция f(x) не определена.

Answer 1

PascalABC.net

var x,y:real;
begin
write('Введите x: ');
readln(x);
if (x>=-2) and (x<=-1)  then y:=2*x+4;
if (x>-1) and (x<=1)  then y:=2*x*x;
if (x>1) and (x<=2)  then y:=-2*x+2;
if (x<-2) or (x>2) then
   writeln('Функция не определена')
   else writeln('f(x)=',y);
end.

Answer 2

Algorithm and Program to Compute the Function f(x)

To compute the function f(x) for a given value of x, we can follow the algorithm below:

1. Start by checking if x is less than or equal to -2. If it is, then f(x) is not defined. Return an appropriate message indicating that the function is not defined for the given value of x.

2. If x is not less than or equal to -2, check if x is between -1 and 1 (inclusive). If it is, then f(x) is equal to 2x^2. Compute the value of f(x) using this formula.

3. If x is not between -1 and 1, check if x is between 1 and 2 (inclusive). If it is, then f(x) is equal to -2x + 2. Compute the value of f(x) using this formula.

4. If x is not between 1 and 2, check if x is greater than 2. If it is, then f(x) is not defined. Return an appropriate message indicating that the function is not defined for the given value of x.

5. Return the computed value of f(x).

Here is an example program in Python that implements the above algorithm:

def compute_f(x):
    if x <= -2:
        return "The function is not defined for x <= -2."
    elif -1 <= x <= 1:
        return 2 * x ** 2
    elif 1 < x <= 2:
        return -2 * x + 2
    else:
        return "The function is not defined for x > 2."

# Example usage
x = 0.5
result = compute_f(x)
print(f"f({x}) = {result}")

Please note that the above program assumes that the input value of x is a floating-point number. If you are working with integers, you can modify the program accordingly.

I hope this helps! Let me know if you have any further questions.