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:?

Question

(r o q)(1)=(q o r)(1)=

Saul Waters · Accepted Answer

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) + 3If 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 + 14If we evaluate that with x = 1 we get q o r(1) = 1 + 6 + 14 = 21

Saul Waters · Answer

(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) = 3and (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

Saul Waters · Answer

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= 9and(r o q)(1) = r( q(1) )= r( 1^2 + 5 )= r(6)= √(6+3)= √9= 3et voilà, mademoiselle !! 😉hope it’ ll help !!PS : if you want good and complete answers don’t forget to give BAs too !! 😉

Ms. Mara Collier

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:?

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