Question

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Answer 1

Answer:

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

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

Step-by-step explanation:

1st problem:

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

r(7) means to replace x in $\sqrt{x+9}$ with 7.

$r(7)=\sqrt{7+9}=\sqrt{16}=4$

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

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 $\sqrt{x+9}$ with 55.

$r(55)=\sqrt{55+9}=\sqrt{64}=8$

Therefore,

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