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 \(\displaystyle{2}{x}-{1}\)

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 \(\displaystyle{2}{x}-{1}\)