Question

the function ( h(x) ) is given. ( h(x)={(3, -5), (5, -7), (6, -9), (10, -12), (12, -16)} ) which of the following gives ( h^{-1}(x) )?

Explanation:

Step1: Recall the definition of inverse function

To find the inverse of a function given as a set of ordered pairs, we swap the \(x\)-coordinate and the \(y\)-coordinate of each ordered pair. That is, if \((a,b)\) is in the function \(h(x)\), then \((b,a)\) will be in \(h^{-1}(x)\).

Step2: Apply the rule to each ordered pair in \(h(x)\)

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

• For \((3,-5)\), swapping gives \((-5,3)\)
• For \((5,-7)\), swapping gives \((-7,5)\)
• For \((6,-9)\), swapping gives \((-9,6)\)
• For \((10,-12)\), swapping gives \((-12,10)\)
• For \((12,-16)\), swapping gives \((-16,12)\)

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

Answer:

\(\{(-5, 3), (-7, 5), (-9, 6), (-12, 10), (-16, 12)\}\) (the first option among the given choices)