6.        Determine what value of the constant ‘ a ‘ makes the function  f(x) = piecewise(`<=`(1, x), `+`(`*`(3, `*`(`^`(x, 2)))), `<`(x, 1), `+`(`*`(a, `*`(x)), `-`(4))); continuous everywhere. 

restart;  

f := proc (x) options operator, arrow, function_assign; piecewise(`<=`(1, x), `+`(`*`(3, `*`(`^`(x, 2)))), `<`(x, 1), `+`(`*`(a, `*`(x)), `-`(4))) end proc;  

f := proc (x) options operator, arrow; piecewise(`<=`(1, x), `+`(`*`(3, `*`(`^`(x, 2)))), `<`(x, 1), `+`(`*`(a, `*`(x)), `-`(4))) end proc; (5.6.1)
 

 

f(x); undefined;  

f(x); 3; f(x); `+`(a, `-`(4));  

`+`(a, `-`(4)) = 3; a = 7;  

algsubs(a = 7, f(x));  

piecewise(`<=`(1, x), `+`(`*`(3, `*`(`^`(x, 2)))), `<`(x, 1), `+`(`*`(7, `*`(x)), `-`(4))); (5.6.2)
 

iscont(%, x = `+`(`-`(infinity)) .. infinity);  

true; (5.6.3)