# To find: The inverse of the given expression f(x)=\frac{x+1}{2}

To find: The inverse of the given expression
$$\displaystyle{f{{\left({x}\right)}}}={\frac{{{x}+{1}}}{{{2}}}}$$

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Step 1
Let $$\displaystyle{y}={a}{x}$$ be a function. The inverse of the function can be found by the replacing the variables of the function.
The inverse of the function $$\displaystyle{y}={a}{x}$$ is $$\displaystyle{x}={a}{y}$$
Consider the given expression.
$$\displaystyle{y}={\frac{{{x}+{1}}}{{{2}}}}$$
Replace the variable y to x and solve it.
$$\displaystyle{x}={\frac{{{y}+{1}}}{{{2}}}}$$
$$\displaystyle{2}{x}={y}+{1}$$
$$\displaystyle{y}={2}{x}-{1}$$
Therefore, the inverse of the given expression is $$\displaystyle{2}{x}-{1}$$