- #1

Jaco Viljoen

- 160

- 9

## Homework Statement

Suppose the functions g and h are defined as follows:

g(x)=-(1/2)x-3

h(x)=√(2-x)

^{2}+(1/2)x

Write down Dh, Dg+h and solve the equation (g+h)(x)=0

## Homework Equations

g(x)=-(1/2)x-3

h(x)=√(2-x)

^{2}+(1/2)x

(g+h)(x)=0

## The Attempt at a Solution

Dg is a line (-∞,∞)

h(x) is two lines that come to a point (2,1) but Dh (-∞,∞)?(I am uncertain if I am correct)

(g+h)(x)=0

(-(1/2)x-3)+(√{(2-x)

^{2}}+(1/2)x)=0

-3+√{(2-x)(2-x)}=0

-3+√{4-2x-2x+x

^{2}}=0

-3+√{x

^{2}-4x+4}=0

√{x

^{2}-4x+4}=3

x

^{2}-4x+4=3

^{2}

x

^{2}-4x+4=9

x

^{2}-4x+4-9=0

x

^{2}-4x-5=0

(x+1)(x-5)=0

x=-1 or x=5

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