37. $$ f(x)=\frac{4}{3} x-9 $$, what is. $$ f^{-1}(-3) $$ ? a. -13 b. -9.5 c. -7 d. 4.5

Question

UpStudy AI · Accepted Answer

To find $$ f^{-1}(-3) $$ for the function $$ f(x) = \frac{4}{3}x - 9 $$, we need to determine the value of $$ x $$ such that $$ f(x) = -3 $$.

**Step 1: Set up the equation**

$$
\frac{4}{3}x - 9 = -3
$$

**Step 2: Solve for $$ x $$**

1. Add 9 to both sides:

$$
\frac{4}{3}x = -3 + 9
$$
$$
frac{4}{3}x = 6
$$

2. Multiply both sides by $$ \frac{3}{4} $$ to isolate $$ x $$:

$$
x = 6 \times \frac{3}{4}
$$
$$
x = \frac{18}{4}
$$
$$
x = 4.5
$$

**Conclusion:**

$$ f^{-1}(-3) = 4.5 $$

**Answer:**  
d. 4.5
$$ f^{-1}(-3) = 4.5 $$

, what is. ?
a. -13
b. -9.5
c. -7
d. 4.5