All categories

3 years ago

Determine whether each of the following functions is even, odd, or neither even nor odd.

Mathematics

1 answer:

Illusion [34]3 years ago

5 0

Answer:

A.) Even.

Step-by-step explanation:

If a function is an even function, then

F(-x) = f(x)

Also, if a function is an odd function, then, f(-x) = -f(x)

You are given the below function

f(x) = 1 + 3x^2 − x^4

Let x = 2

Substitute 2 for x in the function

F(x) = 1 + 3(2)^2 - (2)^4

F(x) = 1 + 3(4) - 16

F(x) = 1 + 12 - 16

F(x) = -3

Also, Substitute -2 for x in the function

F(x) = 1 + 3(-2)^2 - (-2)^4

F(x) = 1 + 3(4) - 16

F(x) = 1 + 12 - 16

F(x) = -3

Since f(-x) = f(x), we can conclude that

F(x) = 1 + 3x^2 - x^4 is even

You might be interested in

A tank contains 100 gal of brine made by dissolving 80 Ib of salt in water. Pure water runs into the tank at the rate of 4 gal/m

ohaa [14]

Answer:

Step-by-step explanation:

Amount of brine = 100 gal

amount of salt = 80 lb

rate of water running = 4 gal / min

Let A be the amount of salt in lb in the tank at any time t.

(a) dA/dt = rate of salt in - rate of salt out

Rate of salt in = 0

rate of salt out = A x 4 / 100 = A / 25 lb/min

So, dA/dt = 0 - A/25 = - A/25 lb/min

$\frac{dA}{A}=-\frac{1}{25}dt$

$\int \frac{dA}{A}=-\frac{1}{25}\int dt$

$A(t) = C e^{-0.04t}$

When t = 0, A = 80 lb

So,

$A(t) = 80 e^{-0.04t}$

(b) Now, A = 40 lb

So,

$40 = 80 e^{-0.04t}$

$0.5 = e^{-0.04t}$

take log on both the sides

$ln 0.5 = - 0.04 t$

t = 17.3 minutes

8 0

3 years ago

Simplify the following expression by combining liker terms: 4x +9 -6x +6

Oxana [17]

Answer:

its very simple you just need to collect like terms...

which is 4x-6x+6+9 which is

-2x+15.

This is my answer I hope it helps you.

6 0

3 years ago

Read 2 more answers

Find area of a parallelogram with a height of 8 inches and a base of 14 inches

12345 [234]

Answer:

$\boxed{ \bold{ \huge{ \boxed{ \sf{112 \: {inches} \: ^{2} }}}}}$

Step-by-step explanation:

Given,

Height of a parallelogram ( h ) = 8 inches

Base of a parallelogram ( b ) = 14 inches

Area of a parallelogram ( A ) = ?

Finding the area of a parallelogram

$\boxed{ \sf{area \: of \: parallelogram \: = \: base \: \times \: height}}$

⇒ $\sf{area \: of \: parallelogram \: = \: 14 \: \times 8}$

⇒ $\sf{area \: of \: parallelogram = 112 \: {inches}^{2} }$

Hope I helped!

Best regards! :D

4 0

3 years ago

What equation represents the line that passes through points (1.-5) and (3 -17)?

zzz [600]

ALL LINES CAN BE REPRESENTED IN THE FORM $f(x) = ax+b$ .

We know that:

$f(1) = -5 \implies a\cdot(1)+b = -5 \implies a+b = -5$

and

$f(3) = -17 \implies a\cdot(3) +b = -17 \implies 3a+b = 17$

Observe that:

$3a+b = 2a+a+b = 2a+(a+b)$

So:

$2a+(a+b) =-17$

But we know that $a+b = -5$ , so:

$2a+(a+b) =-17$

$2a+(-5) = -17$

$2a = -12$

$a = -6$

Since:

$a+b = -5$

$(-6)+b = -5$

$b = 1$

So the line is:

$f(x) = 1-6x$

5 0

3 years ago

Line m passes through points (2,-5) and (4,-3). Line n passes through points (-4,-8) and (-6,-6). Are lined m and n perpendicula

DENIUS [597]

The answer for that is C

4 0

3 years ago