Question

The head circumference 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 height H.
(b) Verify that C = C(H) is the inverse of H = H(C) by showing that H(C(H)) = H and C(H(C)) = C.
(c) Predict the head circumference of a child who is 26 inches tall.

Answer 1

H=2.15C-10.53
2.15C=H+10.53
C=(H+10.53)/2.15

Answer 2

H(C(H))
=H((H+10.53)/2.15)
=2.15(H+10.53)/2.15-10.53
=H

therefore, H(C(H)) = H
also,
C(H(C))
=C(2.15C – 10.53)
=((2.15C-10.53)+10.53)/2.15
=C
therefore, C(H(C)) = C

Answer 3

FROM Q1, C(H) =(H+10.53)/2.15
WHEN , H =26,
C(26) =(26+10.53)/2.15
=17.0

Answer 4

thank you

Answer 5

welcome!