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

deliredejoker7m 2021-11-13 Answered
To find: The inverse of the given expression
\(\displaystyle{f{{\left({x}\right)}}}={\frac{{{x}+{1}}}{{{2}}}}\)

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Expert Answer

Mary Moen
Answered 2021-11-14 Author has 8633 answers
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 \(\displaystyle{2}{x}-{1}\)
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