All categories

3 years ago

Which of the following is an even function?

2 answers:

8 0

Even means g(-x)=g(x)
replace x with -x and see if it simplifies to original functin

g(-x)=(-x-1)²+1
g(-x)=((-1)(x+1))²+1
g(-x)=(x+1)²+1
nope

g(x)=2x²+1
g(-x)=2(-x)²+1
g(-x)=2x²+1
yep

we are done

answer is 2nd one

IrinaVladis [17]3 years ago

8 0

Answer:

2nd Option is correct.

Step-by-step explanation:

We need to find Even function from given functions.

Even function: Even function is a function which hold the following equation.

f(x) = f(-x) for all value of x.

Option 1).

g(x) = ( x - 1 )² + 1 = x² - 2x + 1 + 1 = x² - 2x + 2

put x = -x

g(-x) = (-x)² - 2(-x) + 2 = x² + 2x + 2

Since, g(x) ≠ g(-x)

This is not even function.

Option 2).

g(x) = 2x² + 1

put x = -x

g(-x) = 2(-x)² + 1 = 2x² + 1

Since, g(x) = g(-x)

This is even function.

Option 3).

g(x) = 4x + 2

put x = -x

g(-x) = 4(-x) + 2= -4x + 2

Since, g(x) ≠ g(-x)

This is not even function.

Option 4).

g(x) = 2x

put x = -x

g(-x) = 2(-x) = 2x

Since, g(x) ≠ g(-x)

This is not even function.

Therefore, 2nd Option is correct.

You might be interested in

In the coordinate plane, the point A, 4− 2 is translated to the point A′, 1− 5. Under the same translation, the points B, 7− 4 a

Inga [223]

Answer:

The coordinates of B' and C' are $B'(x,y) = (4, -7)$ and $C'(x,y) = (-1, -8)$ , respectively.

Step-by-step explanation:

From the Linear Algebra, we define the translation of a given point as:

$O'(x,y) = O(x,y) + T(x,y)$ (1)

Where:

$O(x,y)$ - Original point, dimensionless.

$T(x,y)$ - Translation vector, dimensionless.

$O'(x,y)$ - Translated point, dimensionless.

If we know that $A'(x,y) = (1, -5)$ and $A(x,y) = (4,-2)$ , then the translation vector is:

$T(x,y) = A'(x,y)-A(x,y)$ (2)

$T(x,y) = (1,-5)-(4,-2)$

$T(x,y) = (-3,-3)$

If we know that $B(x,y) = (7,-4)$ , $C(x,y) = (2,-5)$ and $T(x,y) = (-3,-3)$ , then the translated points are, respectively:

$B'(x,y) = B(x,y)+T(x,y)$ (3)

$B'(x,y) = (7,-4) +(-3,-3)$

$B'(x,y) = (4, -7)$

$C'(x,y) = C(x,y) +T(x,y)$

$C'(x,y) = (2,-5) + (-3,-3)$

$C'(x,y) = (-1, -8)$

The coordinates of B' and C' are $B'(x,y) = (4, -7)$ and $C'(x,y) = (-1, -8)$ , respectively.

5 0

3 years ago

A car purchased for $17,500. After each year the resale value decreases by 20%. What will the resale value be after 4 years? Rou

Tema [17]

The value at the end of the year is 100% - 20% = 0.80 of the value at the beginning of the year. After 4 years of multiplying by this factor, the value is
$17,500·0.80⁴ = $7,168

3 0

3 years ago

What is the value of log, 81? N け間 w оооо ол

kramer

Answer:

1.908

Step-by-step explanation:

Assuming you are going at a base of 10,

㏒81 = 1.908, just use a calculator

7 0

3 years ago

3. What equation matches the known dimensions of the prism below? Volume: 36 in 3 ? in . (3 in. 4 in. 36 ? x 4 = 3 4x 3 x 36 = ?

alexdok [17]

Answer:

i think its 4 × 3 × ? = 36

Step-by-step explanation:

i hope this helps

if not i am really sorry

7 0

2 years ago

2. Jill works for Fast Food Inc. and earns $332 per week and is paid bi-weekly. How much is deducted

adoni [48]

Answer:

Social Security: $9.63

Step-by-step explanation:

5 0

3 years ago