Consider the functionf(x)=α-x2, x3.f(x) = \left\{\begin{a…
Consider the functionf(x)=α-x2, x3.f(x) = \left\{\begin{array}{ll} \alpha-x^2, \qquad & x < 3, \\ 1, & x=3, \\ 2x+\beta,\quad & x> 3.\end{array}\right.(a) Calculate f(3)f(3), limx→3-f(x)\lim_{x\rightarrow 3^-}f(x) and limx→3+f(x).\lim_{x\rightarrow 3^+}f(x). Your answer may be in terms of α\alpha and β\beta.(b) Find values for α\alpha and β\beta so that f is right continuous, but not continuous at x=3. Justify your answer using the definition of continuity.