Functions?

0 ⤊

1. Find h(k(x)) and k(h(x))
h(x) = 1/2(3x+5)
k(x) = (2x-5) /3x

2. The state the relationship between h and k

2007-09-22 05:40:58 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics

2 answers

h(k(x)) = 1/2(3[(2x-5) /3x]+5)

k(h(x)) = (2[1/2(3x+5)]-5) /3[1/2(3x+5)]

2007-09-22 06:02:57 · answer #1 · answered by mikedotcom 5 · 0⤊ 0⤋

h(x) = 1/2(3x+5) = 1.5x+2.5
k(x) = (2x-5) /3x
h(k(x)) = 1.5(2x-5)/3x +2.5 =(3x - 7.5)/3x +2.5 =(10.5x-7.5)/3x

k(h(x))= (2(1.5x +2.5)-5)/(3(1.5x+2.5))
= (3x)/(4.5x+7.5)

h(x) is a straight line and is continuous everywhere
k(x) is a hyperbola with horizonta asymptote at y = 1/3 and vertcal asymptote at x=0.

2007-09-22 13:26:19 · answer #2 · answered by ironduke8159 7 · 0⤊ 0⤋