Answer:
f(x) = -x is odd
Step-by-step explanation:
A function f is odd if f(-x) = -f(x) for all x in the domain of f. Then, let's check each of the functions.
1. f(x) = x^3 + 5x^2 + x
f(-x) = (-x)^3 + 5(-x)^2 + (-x) = -x^3 + 5x^2 - x
-f(x) = -(x^3 + 5x^2 + x) = -x^3 - 5x^2 - x
Given that f(-x) ≠ -f(x). The function f is not odd.
2. f(x) = sqrt(x)
f(-x) = sqrt(-x) (Imaginary number)
-f(x) = -sqrt(x)
Given that f(-x) ≠ -f(x). The function f is not odd.
3. f(x) = x^2 + x
f(-x) = (-x)^2 -x = x^2 - x
-f(x) = -x^2 - x
Given that f(-x) ≠ -f(x). The function f is not odd.
4. f(x) = -x
f(-x) = - (-x) = x
-f(x) = -(-x) = x
Given that f(-x) = -f(x). The function f is odd.
Answer with Step-by-step explanation:
A function f is odd if:
f(-x)= -f(x) for all x in the domain of f
1. f(x)=
f(-x)=
=
-f(x)=
f(-x) ≠ -f(x)
So, function is not odd
2. f(x)=√x
f(-x)=√(-x)
= i√x
-f(x)= -√x
f(-x) ≠ -f(x)
So, function is not odd
3. f(x)=
f(-x)=
=
-f(x)=
f(-x) ≠ -f(x)
So, function is not odd
4. f(x)= -x
f(-x) = -(-x)
=x
-f(x)=x
f(-x) = -f(x)
So, function is odd
Answer:
slope 3/1
Step-by-step explanation:
Using a graphing calculator (desmos), input the points. Do rise over run and you'll get 3/1
Answer:x=1,y=3
Step-by-step explanation:
Answer:
Step-by-step explanation:
step 1
Find the equation of the first inequality
Find the equation of the first solid line
we have the ordered pairs
(0,-2) and (2,0)
Find the slope
The formula to calculate the slope between two points is equal to
substitute the values
The equation in slope intercept form is equal to
we have
---> the y-intercept is given
substitute
Remember that
Everything to the left of the solid line is shaded
so
The inequality is
step 2
Find the equation of the second inequality
Find the equation of the second dashed line
we have the ordered pairs
(0,2) and (4,0)
Find the slope
The formula to calculate the slope between two points is equal to
substitute the values
The equation in slope intercept form is equal to
we have
---> the y-intercept is given
substitute
Remember that
Everything below and to the left of the line is shaded
so
The inequality is
Rewrite
Multiply by 2 both sides
therefore
The system of inequalities is
see the attached figure to better understand the problem
Answer:
17 1st option
35 2nd option
Step-by-step explanation: