Why isn't my function evaluating to an explicit number?

Question

I'm just wondering why my function is not evaluating as I think it should. I put in the following:

dp = {{0, 71}, {1, 71}, {2, 71}, {3, 70}, {4, 69}, {5, 67}, {6,65}, {7, 63},
{8, 61}, {9, 60}, {10, 60}, {11, 61}, {12, 63},
{13,65}, {14, 66}, {15, 67}, {16, 67}, {16, 67}, {17, 66}, {18,65}, {19, 63},
{20, 60}, {21, 58}, {22, 56}, {23, 55}};
f = Fit[dp, {1, x, x^2, x^3, x^4, x^5, x^6, x^7}, x];
f[3]

but as output I get

(71.121 - 1.29633 x + 1.34837 x^2 - 0.504693 x^3 + 0.0700859 x^4 -
0.00447611 x^5 + 0.000134178 x^6 - 1.53469*10^-6 x^7)[3]

The output I want is the polynomial's value at x=3.

Answer 1

You can just make f a function of x in the first place.

f[x_] = Fit[dp, {1, x, x^2, x^3, x^4, x^5, x^6, x^7}, x]
f[3]
DownValues@f

71.121 - 1.29633 x + 1.34837 x^2 - 0.504693 x^3 + 0.0700859 x^4 - 0.00447611 x^5 + 0.000134178 x^6 - 1.53469*10^-6 x^7

70.4244

{HoldPattern[f[x_]] :> 71.121 - 1.29633 x + 1.34837 x^2 - 0.504693 x^3 + 0.0700859 x^4 - 0.00447611 x^5 + 0.000134178 x^6 - 1.53469*10^-6 x^7}

Also, I guess to actually answer your question of why it happened...It's because you were setting f as the polynomial expression itself, rather than a function of x. One could alternatively do

f = Fit[dp, {1, x, x^2, x^3, x^4, x^5, x^6, x^7}, x]
f /. x -> 3

71.121 - 1.29633 x + 1.34837 x^2 - 0.504693 x^3 + 0.0700859 x^4 - 0.00447611 x^5 + 0.000134178 x^6 - 1.53469*10^-6 x^7

70.4244

Or even

f = Function[x, Evaluate@Fit[dp, {1, x, x^2, x^3, x^4, x^5, x^6, x^7}, x]]
f[3]

Function[x, 71.121 - 1.29633 x + 1.34837 x^2 - 0.504693 x^3 + 0.0700859 x^4 - 0.00447611 x^5 + 0.000134178 x^6 - 1.53469*10^-6 x^7]

70.4244