Question

If h = {(1,5), (-2,6), (4, -3), (6,9)} and

m = {(3,4), (2,-2), (-2,6), (5,8)}, what is (hm) (2)? (See image below)

Answer 1

Answer:
`(h\circ m)(2) = 6`

=======================================================

Step-by-step explanation:

The notation
`(h \circ m)(2)` refers to function composition

It's the same as writing
`h(m(2))`

According to

m = {(3,4), (2,-2), (-2,6), (5,8)}

We have m(2) = -2 since x = 2 leads to m(x) = -2

Then the output -2 is treated as the input of the outer function h(x)

Looking through

h = {(1,5), (-2,6), (4, -3), (6,9)}

shows that h(-2) = 6

Therefore,
`h(m(2)) = h(-2) = 6, \ \text{ and } \ (h\circ m)(2) = 6`

Optionally we can write out a table like shown below.

The row highlighted shows the input x = 2 leading to m(x) = -2, which is then plugged into h(x) to get 6 as the final output. Think of it like a chain of dominoes.