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)?
{(3, 5), (5, 7), (6, 9), (10, 12), (12, 16)}
{(–5, 3), (–7, 5), (–9, 6), (–12, 10), (–16, 12)}
{(3, –5), (5, –7), (6, –9), (10, –12), (12, –16)}
{(5, 3), (7, 5), (9, 6), (12, 10), (16, 12)}

Answer 1

B.) {(–5, 3), (–7, 5), (–9, 6), (–12, 10), (–16, 12)}

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Answer 2

The correct option is 2.

Explanation:

The given function is

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

If coordinates of a function is defined as (x,y), then the coordinates of its inverse is defined as (y,x).

`(x,y)\rightarrow (y,x)`

`(3,-5)\rightarrow (-5,3)`

`(5,-7)\rightarrow (-7,5)`

`(6,-9)\rightarrow (-9,6)`

`(10,-12)\rightarrow (-12,10)`

`(12,-16)\rightarrow (-16,12)`

The inverse of the given function is

h⁻¹(x) = {(–5, 3), (–7, 5), (–9, 6), (–12, 10), (–16, 12)}

Therefore option 2 is correct.