Question

If $f\left(x\right)=\frac{1}{3}x+3$, then find $f^{-1}\left(x\right)$.

• A. $-\frac{1}{3}x-3$
• B. $-3x+\frac{1}{3}$
• C. $3x+\frac{1}{3}$
• D. $3x-3$
• E. $3x-9$

Answer 1

The correct option is E $3x-9$

$f\left(x\right)=\frac{1}{3}x+3$

Let the equation be $y$, then we get

$f\left(x\right)=\frac{1}{3}x+3=y$

Therefore $f^{-1}y=x$
$\therefore \frac{1}{3}x+3=y$

$\therefore x=3(y-3)$
$\therefore f^{-1}y=x=3(y-3)$

Now replace $y$ with $x$.
So, the answer is $3x-9$.