Question

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Answer 1

`(q \circ r)(7)=22`

`(r \circ q)(7)=8`

Explanation:

1st problem:

`(q \circ r)(7)=q(r(7))`

r(7) means to replace x in
`√(x+9)` with 7.

`r(7)=√(7+9)=√(16)=4`

`(q \circ r)(7)=q(r(7))=q(4)`

q(4) means replace x in
`x^2+6` with 4.

`q(4)=4^2+6=16+6=22`.

Therefore,

`(q \circ r)(7)=q(r(7))=q(4)=22`

2nd problem:

`(r \circ q)(7)=r(q(7))`

q(7) means replace x in
`x^2+6` with 7.

`q(7)=7^2+6=49+6=55`.

So now we have:

`(r \circ q)(7)=r(q(7))=r(55)`.

r(55) means to replace x in
`√(x+9)` with 55.

`r(55)=√(55+9)=√(64)=8`

Therefore,

`(r \circ q)(7)=r(q(7))=r(55)=8`.