Math / Algebra

QuestionThe table below gives values of an invertible function $f(x)$ : \begin{tabular}{|cccccc|} \hline $x$ & -2 & -1 & 0 & 1 & 2 \\ $f(x)$ & -3 & 4 & 2 & 5 & 0 \\ \hline \end{tabular} (a) $f(0)=$ $\square$ (b) $f(\square)=0$ (c) $f^{-1}(0)=$ $\square$ (d) $f^{-1}(\square)=0$ $\square$

Studdy Solution

STEP 1

1. We are given a table of values for an invertible function $f(x)$ .
2. We need to find specific values and inverses based on the table.

STEP 2

1. Use the table to find the value of $f(0)$ .
2. Use the table to find the value of $x$ such that $f(x) = 0$ .
3. Determine $f^{-1}(0)$ using the table.
4. Determine $f^{-1}(x)$ such that $f(x) = 0$ .

STEP 3

Look at the table to find $f(0)$ .
From the table, when $x = 0$ , $f(x) = 2$ .
Thus, $f(0) = 2$ .

STEP 4

Look at the table to find $x$ such that $f(x) = 0$ .
From the table, when $x = 2$ , $f(x) = 0$ .
Thus, $f(\square) = 0$ where $\square = 2$ .

STEP 5

Determine $f^{-1}(0)$ .
Since $f(2) = 0$ , then $f^{-1}(0) = 2$ .

STEP 6

Determine $f^{-1}(x)$ such that $f(x) = 0$ .
Since $f(2) = 0$ , then $f^{-1}(\square) = 0$ where $\square = 2$ .
The answers are: (a) $f(0) = 2$ (b) $f(2) = 0$ (c) $f^{-1}(0) = 2$ (d) $f^{-1}(2) = 0$

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QuestionThe table below gives values of an invertible function $f(x)$ : \begin{tabular}{|cccccc|} \hline $x$ & -2 & -1 & 0 & 1 & 2 \\ $f(x)$ & -3 & 4 & 2 & 5 & 0 \\ \hline \end{tabular} (a) $f(0)=$ $\square$ (b) $f(\square)=0$ (c) $f^{-1}(0)=$ $\square$ (d) $f^{-1}(\square)=0$ $\square$

Studdy Solution

STEP 1

1. We are given a table of values for an invertible function $f(x)$ .
2. We need to find specific values and inverses based on the table.

STEP 2

1. Use the table to find the value of $f(0)$ .
2. Use the table to find the value of $x$ such that $f(x) = 0$ .
3. Determine $f^{-1}(0)$ using the table.
4. Determine $f^{-1}(x)$ such that $f(x) = 0$ .

STEP 3

Look at the table to find $f(0)$ .
From the table, when $x = 0$ , $f(x) = 2$ .
Thus, $f(0) = 2$ .

STEP 4

Look at the table to find $x$ such that $f(x) = 0$ .
From the table, when $x = 2$ , $f(x) = 0$ .
Thus, $f(\square) = 0$ where $\square = 2$ .

STEP 5

Determine $f^{-1}(0)$ .
Since $f(2) = 0$ , then $f^{-1}(0) = 2$ .

STEP 6

Determine $f^{-1}(x)$ such that $f(x) = 0$ .
Since $f(2) = 0$ , then $f^{-1}(\square) = 0$ where $\square = 2$ .
The answers are: (a) $f(0) = 2$ (b) $f(2) = 0$ (c) $f^{-1}(0) = 2$ (d) $f^{-1}(2) = 0$

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Studdy Solution

STEP 1

1. We are given a table of values for an invertible function f(x) f(x) f(x).2. We need to find specific values and inverses based on the table.

STEP 2

1. Use the table to find the value of f(0) f(0) f(0).2. Use the table to find the value of x x x such that f(x)=0 f(x) = 0 f(x)=0.3. Determine f−1(0) f^{-1}(0) f−1(0) using the table.4. Determine f−1(x) f^{-1}(x) f−1(x) such that f(x)=0 f(x) = 0 f(x)=0.

STEP 3

Look at the table to find f(0) f(0) f(0).From the table, when x=0 x = 0 x=0, f(x)=2 f(x) = 2 f(x)=2.Thus, f(0)=2 f(0) = 2 f(0)=2.

STEP 4

Look at the table to find x x x such that f(x)=0 f(x) = 0 f(x)=0.From the table, when x=2 x = 2 x=2, f(x)=0 f(x) = 0 f(x)=0.Thus, f(□)=0 f(\square) = 0 f(□)=0 where □=2 \square = 2 □=2.

STEP 5

Determine f−1(0) f^{-1}(0) f−1(0).Since f(2)=0 f(2) = 0 f(2)=0, then f−1(0)=2 f^{-1}(0) = 2 f−1(0)=2.

STEP 6

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1. We are given a table of values for an invertible function $f(x)$ .
2. We need to find specific values and inverses based on the table.

1. Use the table to find the value of $f(0)$ .
2. Use the table to find the value of $x$ such that $f(x) = 0$ .
3. Determine $f^{-1}(0)$ using the table.
4. Determine $f^{-1}(x)$ such that $f(x) = 0$ .

Look at the table to find $f(0)$ .
From the table, when $x = 0$ , $f(x) = 2$ .
Thus, $f(0) = 2$ .

Look at the table to find $x$ such that $f(x) = 0$ .
From the table, when $x = 2$ , $f(x) = 0$ .
Thus, $f(\square) = 0$ where $\square = 2$ .

Determine $f^{-1}(0)$ .
Since $f(2) = 0$ , then $f^{-1}(0) = 2$ .