The image contains the following mathematical problem:

"Diketahui $f(x) = 3 - 2x$ dan $g(x) = 5x + 1$. Tentukan $(f \circ g)^{-1}(x)$ serta tentukan $(f \circ g)^{-1}(-9)$."

This translates to:

"Given $f(x) = 3 - 2x$ and $g(x) = 5x + 1$, determine $(f \circ g)^{-1}(x)$ and $(f \circ g)^{-1}(-9)$."

Solution:

1. Find $f(g(x))$:

   To find the composition $f \circ g(x)$, substitute $g(x)$ into $f(x)$: $f(g(x)) = f(5x + 1) = 3 - 2(5x + 1)$ Simplify the expression: $f(g(x)) = 3 - 10x - 2 = 1 - 10x$ So, $f \circ g(x) = 1 - 10x$.

2. Find the inverse of $f(g(x))$:

   Let $y = f(g(x)) = 1 - 10x$. To find the inverse, solve for $x$ in terms of $y$: $y = 1 - 10x$ $10x = 1 - y$ $x = \frac{1 - y}{10}$ Therefore, the inverse function is: $(f \circ g)^{-1}(x) = \frac{1 - x}{10}$

3. Find $(f \circ g)^{-1}(-9)$:

   Substitute $x = -9$ into the inverse function: $(f \circ g)^{-1}(-9) = \frac{1 - (-9)}{10} = \frac{1 + 9}{10} = \frac{10}{10} = 1$

Final Answers:

• $(f \circ g)^{-1}(x) = \frac{1 - x}{10}$
• $(f \circ g)^{-1}(-9) = 1$

Would you like any more details or have any questions?

Here are 5 related questions:

1. How do you find the inverse of a general linear function?
2. What is the significance of function composition in mathematical analysis?
3. Can you find the inverse of a quadratic function? How does it differ?
4. How does the composition of functions affect their domain and range?
5. What are the steps to verify if two functions are inverses of each other?

Tip: Always remember to check the domain and range when working with inverse functions to ensure they are properly defined.