Let \(f:R→R:f(x)=\frac{2x-7}{4}\) be an invertible function. Find f

1.	Let \(f:R→R:f(x)=\frac{2x-7}{4}\) be an invertible function. Find f-1.
Answer» To find: f^-1 Given: \(f:R→R:f(x)=\frac{2x-7}{4}\) We have, \(f(x)=\frac{2x-7}{4}\) Let f(x) = y such that \(y\in R\) \(\Rightarrow y=\frac{2x-7}{4}\) ⇒ 4y = 2x – 7 ⇒ 4y + 7 = 2x \(\Rightarrow x=\frac{4y+7}{2}\) \(\Rightarrow f^{-1}=\frac{4y+7}{2}\) \(f^{-1}(y)=\frac{4y+7}{2}\) for all \(y\in R\)

Let \(f:R→R:f(x)=\frac{2x-7}{4}\) be an invertible function. Find f-1.

Answer»

To find: f^-1

Given: \(f:R→R:f(x)=\frac{2x-7}{4}\)

We have,

\(f(x)=\frac{2x-7}{4}\)

Let f(x) = y such that \(y\in R\)

\(\Rightarrow y=\frac{2x-7}{4}\)

⇒ 4y = 2x – 7

⇒ 4y + 7 = 2x

\(\Rightarrow x=\frac{4y+7}{2}\)

\(\Rightarrow f^{-1}=\frac{4y+7}{2}\)

\(f^{-1}(y)=\frac{4y+7}{2}\) for all \(y\in R\)