Answer
$y=0.75x+1 \\$
Work Step by Step
1. The tangent line at x=a passes through the point (a, f(a))$\\$
(we must first find f(a)$\\$
2. It has slope m$=f^{\prime}(a)\\$
3. Its equation (point slope): $y-f(a)=f^{\prime}(a)(x-a)\\$
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1. $x=2, \ \ \ f(2)$=$2+\displaystyle \frac{1}{2}=2.5.\\$
The point on the graph is $(2,2.5).\\$
2. Slope. $\\$
$f^{\prime}(x)=$ (sum, power rule)$ = [x+x^{-1}]^{\prime}=1-x^{-2}=1-\displaystyle \frac{1}{x^{2}}\\$
$m=f^{\prime}(2)=1-\displaystyle \frac{1}{2^{2}}=0.75\\$
3. Equation. P$(2,2.5),\ m=0.75 \\$
$y-2.5=0.75(x-2) \\$
$y-2.5=0.75x-1.5 \\$
$y=0.75x+1 \\$
image enclosed: graph