Question

the function \\(h(x)\\) is given below.

\\h(x) = \\{(3, -5), (5, -7), (6, -9), (10, -12), (12, -16)\\}\\

which of the following gives \\(h^{-1}(x)\\)?

\\(\bigcirc\\) \\(\\{(3, 5), (5, 7), (6, 9), (10, 12), (12, 16)\\}\\)
\\(\bigcirc\\) \\(\\{(-5, 3), (-7, 5), (-9, 6), (-12, 10), (-16, 12)\\}\\)
\\(\bigcirc\\) \\(\\{(3, -5), (5, -7), (6, -9), (10, -12), (12, -16)\\}\\)
\\(\bigcirc\\) \\(\\{(5, 3), (7, 5), (9, 6), (12, 10), (16, 12)\\}\\)

Explanation:

Define the inverse relation

Using the Inverse Functions knowledge point

$$ h^{-1} = \{(y, x) \mid (x, y) \in h\} $$

Swap the coordinates

Using the Inverse Functions knowledge point

$$
LATEXBLOCK0
$$

Construct the inverse set

Using the Inverse Functions knowledge point

$$ h^{-1}(x) = \{(-5, 3), (-7, 5), (-9, 6), (-12, 10), (-16, 12)\} $$

Answer:

• O \(\{(3, 5), (5, 7), (6, 9), (10, 12), (12, 16)\}\)
• O \(\{(-5, 3), (-7, 5), (-9, 6), (-12, 10), (-16, 12)\}\) (Correct answer)
• O \(\{(3, -5), (5, -7), (6, -9), (10, -12), (12, -16)\}\)
• O \(\{(5, 3), (7, 5), (9, 6), (12, 10), (16, 12)\}\)