Question

Given $f\left(x\right)=7x+5$, solve for $f^{-1}\left(x\right)$, the inverse function.

• A. $f^{-1}\left(x\right)=7x+5$
• B. $f^{-1}\left(x\right)=5x+7$
• C. $f^{-1}\left(x\right)=\frac{1}{7}x+\frac{1}{5}$
• D. $f^{-1}\left(x\right)=\frac{1}{7}x-\frac{1}{5}$
• E. $f^{-1}\left(x\right)=\frac{x-5}{7}$

Answer 1

The correct option is E $f^{-1}\left(x\right)=\frac{x-5}{7}$

Given $f\left(x\right)=7x+5$

Let $f\left(x\right)$ be $y$
$\Rightarrow f\left(x\right)=7x+5=y$

$\Rightarrow x=\frac{(y-5)}{7}$
Since $f\left(x\right)=y$ , $x=f^{-1}\left(y\right)=\frac{(y-5)}{7}$
Therefore $f^{-1}\left(x\right)=\frac{(x-5)}{7}$