The mathematical definition and example of a recursive function f is as follows:

Question

The mathematical definition and example of a recursive function f is as follows: ase case f(0) 5 ecursive case: Example f(1) 2(f (n 1))-3 2(f(0)) 3 2(5)-3 7 Consider the following function prototype for calculating f(n) In a C+ program named recursion.cpp, complete the function prototype using recursion. For full credit, the program must include the following: A true recursive structure (including recursive function calls) Display on console output for each iteration of the factorial calculation, including f(0) and f(n) A comment indicating the base case of the function A comment indicating the recursive case of the function Input validation in the main function for integers greater than or equal to 0 A sample run of the program is shown below: Enter a number greater than or equal to 0 1 Please enter a valid number! Enter a number greater than or equal to 0: 8 f (0) 5 E(1) 7 f (2) 11 E (3) 19 (4) 35 E (5) 67 t (6) 131 £ (7) 259 f (8) 515 Press any key to continue . . .

Explanation / Answer

#include<iostream>

using namespace std;

int f(int n)

{

int f_n=0;//to store return value

if(n==0)

{

f_n = 5;

}

else

{

f_n += 2*f(n-1)-3;

}

cout<<"f("<<n<<") = "<<f_n<<endl;//printing f(n) after a function call is completed

return f_n;

}

int main()

{

int inp;

cout<<"Enter value greater than or equal to -1 : ";

cin>>inp;

if(inp>=0)

{

f(inp);

}

else

{

cout<<"Please Enter a valid number"<<endl;

}

return 0;

}

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