MATH QUESTION please help I’m stumped :( Suppose that functions q and r are defined as follows. q(x)=x^2+5 r(x)=√x+3 find the following:?

(r o q)(1)=

(q o r)(1)=

3 Answers

  1. 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

  2. (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

  3. 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 !! 😉

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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)=?

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-> 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)=?     

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Question 969892: 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)=?
Answer by stanbon(75887)   (Show Source):

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put this solution on YOUR website! 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)=?
= r(2) + q(2)
= sqrt(4) + (4+3) = 9
——————————–
2. (q ◦ r)(2)=?
Answer is the same as above.
========
Cheers,
Stan H.

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