(r o q)(1)=
(q o r)(1)=
3 Answers

q(x) = x^2 + 5
r(x)= √x + 3
The main thig is to understand what r o q(1) and (q o r)(1) mean.
To get r o q we replace the x in r(x)= √x + 3 by q(x) = x^2 + 5
r o q = √(x^2 + 5) + 3
If we evaluate that with x = 1 we get
r o q(1) = √(1^2 + 5) + 5 = 5 + √(6)
In a similar way, but with the functions the other way round,
to get q o r we replace the x in q(x) = x^2 + 5 by r(x)= √x + 3
q o r = (√x + 3)^2 + 5 = 9 + 6√x + x + 5 = x + 6√x + 14
If we evaluate that with x = 1 we get
q o r(1) = 1 + 6 + 14 = 21

(r∘q)(x) = r(q(x))
∴ (r∘q)(x) = √q(x) + 3
∴ (r∘q)(x) = √(x² + 5) + 3
∴ (r∘q)(1) = √(1² + 5) + 3
∴ (r∘q)(1) = √6 + 3
(q∘r)(x) = q(r(x))
∴ (q∘r)(x) = (r(x))² + 5
∴ (q∘r)(x) = (√x + 3)² + 5
∴ (q∘r)(1) = (√1 + 3)² + 5
∴ (q∘r)(1) = (1 + 3)² + 5
∴ (q∘r)(1) = 4² + 5
∴ (q∘r)(1) = 16 + 5
∴ (q∘r)(1) = 21
Now just in case you meant r(x) = √(x + 3) in stead
(r∘q)(x) = r(q(x))
∴ (r∘q)(x) = √(q(x) + 3)
∴ (r∘q)(x) = √((x² + 5) + 3)
∴ (r∘q)(x) = √(x² + 5 + 3)
∴ (r∘q)(x) = √(x² + 8)
∴ (r∘q)(1) = √(1² + 8)
∴ (r∘q)(1) = √9
∴ (r∘q)(1) = 3
and
(q∘r)(x) = q(r(x))
∴ (q∘r)(x) = (r(x))² + 5
∴ (q∘r)(x) = (√(x + 3))² + 5
∴ (q∘r)(x) = x + 3 + 5
∴ (q∘r)(x) = x + 8
∴ (q∘r)(1) = 1 + 8
∴ (q∘r)(1) = 9

Well,
q(x)=x^2+5 r(x) = √(x+3)
therefore :
(q o r)(1) = q( r(1) )
= q( √(1+3) )
= q( √4 )
= q(2)
= 2^2 + 5
= 4 + 5
= 9
and
(r o q)(1) = r( q(1) )
= r( 1^2 + 5 )
= r(6)
= √(6+3)
= √9
= 3
et voilà, mademoiselle !! 😉
hope it’ ll help !!
PS : if you want good and complete answers don’t forget to give BAs too !! 😉
Relevant information
SOLUTION: Suppose that the functions q and r are defined as follows.
q(x)=x^2+3
r(x)=sqrt(x+2)
Find the following.
1. (r ◦ q)(2)=?
2. (q ◦ r)(2)=?
Algebra
>
Functions
> SOLUTION: Suppose that the functions q and r are defined as follows.
q(x)=x^2+3
r(x)=sqrt(x+2)
Find the following.
1. (r ◦ q)(2)=?
2. (q ◦ r)(2)=?
Log On
