Plotting curve of f(α) = (α2 + 1)^(0.5) for t between 0 and 5, using MML to annotate graphic

Question

I need to plot a curve of f(α) = (α2 + 1)^(0.5) for t between 0 and 5, using MML to annotate graphic. Any help would be appreciated, Thanks.

So far I have two options the first shows a curve without the Function annotated at the top. This is with extra parentheses in the comments.

curve((x^2 + 1)^(0.5), from=0, to=5,
      xlab = expression(alpha),
      ylab = expression((alpha^2 + 1)^(0.5), # ((alpha
      main = expression(paste("Function : ",
                              f(alpha) == (alpha^2 + 1)^(0.5))))) # ))

Output:

When I exclude the parentheses commented above one before the alpha and the matching one. I think I would get the annotated function at the top of the curve.

curve((x^2 + 1)^(0.5), from=0, to=5,
      xlab = expression(alpha),
      ylab = expression(alpha^2 + 1)^(0.5),
      main = expression(paste("Function : ",
                              f(alpha) == (alpha^2 + 1)^(0.5))))

The program doesn't run and gives me this error.

Error in expression(alpha^2 + 1)^(0.5) : 
  non-numeric argument to binary operator

Answer 1

I think it may just be placement of parentheses. This should work:

curve((x^2 + 1)^(0.5), from=0, to=5,
      xlab = expression(alpha),
      ylab = expression((alpha^2 + 1)^(0.5)), 
      main = expression(paste("Function : ", f(alpha) == (alpha^2 + 1)^(0.5))))