The given function is even.
Solution:
<em>If f(-x) = f(x), then the function is even.</em>
<em>If f(-x) = -f(x), then the function is odd.</em>
Given function:
Substitute x = -x
= f(x) (given)
f(-x) = f(x)
From the definition, it is even.
Hence the given function is even.
Answer:
The system of inequalities is
Step-by-step explanation:
step 1
Find the equation of the solid line that goes through the points negative 3, 0, negative 4, negative 1
Let
A(-3,0),B(-4,-1)
Find the slope
m=(-1-0)/(-4+3)
m=-1/-1=1
The equation of the line into point slope form is equal to
y-y1=m(x-x1)
we have
m=1
point A(-3,0)
substitute
y-0=(1)(x+3)
y=x+3
The solution is the shaded area below the solid line
therefore
The equation of the first inequality is equal to
step 2
Find the equation of the solid line that goes through the points 1, 1, 2, negative 1
Let
C(1,1),D(2,-1)
Find the slope
m=(-1-1)/(2-1)
m=-2/1=-2
The equation of the line into point slope form is equal to
y-y1=m(x-x1)
we have
m=-2
point C(1,1)
substitute
y-1=(-2)(x-1)
y=-2x+2+1
y=-2x+3
The solution is the shaded area below the solid line
therefore
The equation of the first inequality is equal to
therefore
The system of inequalities is
