Math Problem Statement
Use the table below to fill in the missing values:
1. f(2) = ?
2. If f(x) = 0, then x = ?
3. f^(-1)(-8) = ?
4. If f^(-1)(x) = 7, then x = ?
Solution
Let's analyze the table and solve the questions based on it. The table provides values for and the corresponding function values .
Here's the table extracted from the image:
x & f(x) \\ \hline 0 & 8 \\ 1 & 6 \\ 2 & 4 \\ 3 & 2 \\ 4 & 0 \\ 5 & -2 \\ 6 & -4 \\ 7 & -6 \\ 8 & -8 \\ 9 & -10 \\ \end{array}$$ Now, let's answer the questions: 1. **$$f(2) =$$** To find $$f(2)$$, look for the value of $$f(x)$$ when $$x = 2$$. $$f(2) = 4$$ 2. **If $$f(x) = 0$$, then $$x =$$** To find $$x$$ when $$f(x) = 0$$, look for the value of $$x$$ corresponding to $$f(x) = 0$$. $$f(x) = 0 \text{ when } x = 4$$ 3. **$$f^{-1}(-8) =$$** The inverse function $$f^{-1}(y)$$ gives the value of $$x$$ such that $$f(x) = y$$. $$f^{-1}(-8) = 8$$ 4. **If $$f^{-1}(x) = 7$$, then $$x =$$** If $$f^{-1}(x) = 7$$, then $$f(7) = x$$. Look for the value of $$f(7)$$. $$f(7) = -6 \text{, so } x = -6$$ Here are the answers: 1. $$f(2) = 4$$ 2. If $$f(x) = 0$$, then $$x = 4$$ 3. $$f^{-1}(-8) = 8$$ 4. If $$f^{-1}(x) = 7$$, then $$x = -6$$ Would you like further details on any of these solutions or explanations? --- **Related Questions:** 1. What is $$f^{-1}(0)$$? 2. Find $$f(9)$$. 3. If $$f^{-1}(x) = 4$$, what is $$x$$? 4. Calculate $$f^{-1}(-2)$$. 5. Determine $$f(0)$$. **Tip:** When working with inverse functions, remember that $$f^{-1}(y) = x$$ means $$f(x) = y$$. This helps you find the input $$x$$ that corresponds to a given output $$y$$.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Functions
Inverse Functions
Formulas
f(x) = y
f^{-1}(y) = x
Theorems
Definition of Inverse Functions
Suitable Grade Level
Grades 9-10