Height and Headcircumference: The headcircumference C of a child is related to the height H of the child(both in inches) through the function: H(C) =2.15C-10.53 (a) Express the head circumference C as a function of heightH (b)Verify that C=C(H) is the inverse of H=H(C) by showing thatH(C(H))=H and C(H(C))=C. (c)Predict the head circumference of a child who is 26 inchestall.

sincsenekdq

sincsenekdq

Answered question

2022-09-04

Height and Headcircumference: The headcircumference C of a child is related to the height H of the child(both in inches) through the function:
H(C) =2.15C-10.53
(a) Express the head circumference C as a function of heightH
(b)Verify that C=C(H) is the inverse of H=H(C) by showing thatH(C(H))=H and C(H(C))=C.
(c)Predict the head circumference of a child who is 26 inchestall.

Answer & Explanation

Nelson Santana

Nelson Santana

Beginner2022-09-05Added 13 answers

H ( C ( H ) ) = 2.15 ( H + 10.53 2.15 ) 10.53 = H + 10.53 10.53 = H
a) Solve for c:
C = (H + 10.53)/2.15
C(H) = (H+10.53)/2.15
b) To verify the inverses, you do acomposition that is put one function into the other.
C ( H ( C ) ) = ( 2.15 C 10.53 ) + 10.53 2.15 = 2.15 C 2.15 = C
That shows that the functions "undo" each other.
Now try it the other way,
H ( C ( H ) ) = 2.15 ( H + 10.53 2.15 ) 10.53 = H + 10.53 10.53 = H
c) H=26, find C ( 26 ) = 26 + 10.53 2.15 = 16.99069767
Truscelli3h

Truscelli3h

Beginner2022-09-06Added 1 answers

a- solve for C-> C=(H(C)+10.53)/2.15
b- just pick a number for C, and plug in.
c- plug in 26 inches for the H, and solve for c.

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