Find the value of ''c'' that makes the function continuous?

f(x) = {2x+9} for x%26lt; or equal to 3 and {-4x+c} for x%26gt;3

Find the value of ''c'' that makes the function continuous?
f(3) = 2*3 + 9 = 15


lim f(x) as x approaches 3+ is (-12 + c)





-12 + c = 15


c = 15 +12 = 27





The function will be continuous if c=27.
Reply:f (x) = (2x + 9) being a polynomial is continuous for all values of x %26lt; or equal to 3.





f(x) = - 4x + c being a polynomial is continuous for all values of x %26gt; 3.





Now, for function to be continuous at 3,





Left-hand limit of f(x) at x = 3, right-hand limit of f(x) at x =3 and the value of the function for x =3 must all be equal.





Left-hand limit of f(x) at x = 3 is 2*3 + 9 = 15


Right-hand limit of f(x) at x = 3 is - 4*3 + c = -12 + c


Value of the function at x = 3 is 2*3 + 9 = 15





So, -12 + c = 15


=%26gt; c = 27
Reply:Find the value for c where lim (x→3-) f(x) = lim (x→3+) f(x)


In other words, solve for the equation for c





2(3) + 9 = -4(3) + c


=%26gt; c = 27