Here are two formulas for piecewisedefined functions Use the

Here are two formulas for piecewise-defined functions: Use these formulas to evaluate and solve the following: (give exact values) H(k) = {|k + 6| if k

Solution

A.

for H(2)

H(k) = sqrt (k - 2)

H(2) = sqrt (2 - 2) = 0

B.

m(H(2)) = m(0)

for y = 0,

m(y) = 2y^2 - 4

m(0) = 2*0 ^2 - 4 = -4

C.

m*(3) = 2*y^2 - 4 = 2*3^2 - 4 = 14

D.

H(m(3)) = H(14)

H(k) = sqrt(k - 2)

H(14) = sqrt (14 - 2) = sqrt 12 = 2*sqrt 3

E.

H(-1) = undefined

F.

m(H(-1)) = undefined

G.

m(-2) = -1

H.

H(m(-2)) = H(-1) = undefined

I.

m(-4) = 2*(-4) = -8

J.

H(m(-4)) = H(-8)

H(k) = |k+6|

H(-8) = |-8+6| = |-2|

H(-8) = 2

K.

H(-3) = |=3 + 6| = 3

L.

H(H(-3)) = H(3)

H(3) = sqrt (3 - 2) = 1

M.

H(5)*m(1) = sqrt (5 - 2)*(2*1^2 - 4) = -2*sqrt 3

N.

5*H(5) = 5*sqrt (5 - 2) = 5*sqrt 3

O.

3 + m(1) = 3 + (2*1^2 - 4) = 1

P.

m(3 + H(-4))

H(-4) = |-4 + 6| = 2

m(3 + 2) = m(5) = 2*5^2 - 4 = 46

q.

H(k) = 2

if H(k) = sqrt (k - 2) = 2

k - 2 = 4

k = 6,

if H(k) = |k +6| = 2

k + 6 = 2

k = -4

OR

-(k + 6) = 2

k = -8

R.

m(y) = 5,

if m(y) = 2y = 5

y = 5/2, it\'s not possible since y should be less than -3

if m(y) = 2*y^2 - 5 = 5

2*y^2 = 10

y^2 = 5

y = +sqrt 5