Let
$f (x) = \frac{1}{3} x - 5, 4 \leq x \leq 9$
The domain of $f^{- 1}$ is the interval $[A, B]$ where $A =$ and $B =$

Answer

Expert–verified

Hide Steps

Answer

$[A, B] = [- \frac{11}{3}, - 2]$

Steps

Step 1 ：Let $f (x) = \frac{1}{3} x - 5, 4 \leq x \leq 9$

Step 2 ：The domain of the inverse function $f^{- 1}$ is the range of the original function $f$ .

Step 3 ：To find the range of $f$ , we substitute the endpoints of the domain of $f$ into the function $f$ .

Step 4 ：When $x = 4$ , $f (x) = \frac{1}{3} \times 4 - 5 = - \frac{11}{3}$

Step 5 ：When $x = 9$ , $f (x) = \frac{1}{3} \times 9 - 5 = - 2$

Step 6 ：So, the domain of $f^{- 1}$ is the interval $[A, B]$ where $A = - \frac{11}{3}$ and $B = - 2$

Step 7 ： $[A, B] = [- \frac{11}{3}, - 2]$