All categories

2 months ago

Which of the following is an even function g(x) = (x – 1)2 + 1g(x) = 2x2 + 1g(x) = 4x + 2g(x) = 2x

2 answers:

8 0

An even function can be reflected over the y-axis and still remain unchanged.
Example: y=x^2
On the other hand, an odd function can be reflected around the origin and also remains unchanged.
Example: y=x^3

A straightforward method to determine this is:

if f(x) is even, then f(-x)=f(x)
if f(x) is odd, then f(-x)=-f(x)

Hence, for an even function
substitute -x in for each and check for equivalence
make sure to fully expand the expressions
g(x)=(x-1)^2+1=x^2-2x+1+1=x^2-2x+2 is the original expression
g(x)=(x-1)^2+1
g(-x)=(-x-1)^2+1
g(-x)=(1)(x+1)^2+1
g(-x)=x^2+2x+1+1
g(-x)=x^2+2x+2
Not the same, as the original contains -2x
Therefore, it is not even
g(x)=2x^2+1
g(-x)=2(-x)^2+1
g(-x)=2x^2+1
It matches, hence it is even
g(x)=4x+2
g(-x)=4(-x)+2
g(-x)=-4x+2
Not equivalent, thus not even
g(x)=2x
g(-x)=2(-x)
g(-x)=-2x
Not equal, therefore not even

g(x)=2x²+1 is the confirmed even function.

Inessa [12.5K]2 months ago

4 0

Answer:

The second function is classified as an even function.

Detailed explanation:

The functions provided are

$1.\: g(x)=(x-1)^2+1\\2.\:g(x)=2.x^2+1\\3.\:g(x)=4.x+2\\4.\:g(x)=2.x$

Even functions maintain the same output when the variable is substituted with its negative, meaning f(x) = f(-x)

In this case,

For the first function

$g(x)=(x-1)^2+1\implies g(x)= x^2-2.x+1+1\implies g(x)=x^2-2.x+2$

by substituting x with -x we find

$g(-x)=(-x)^2-2.(-x)+2\\g(-x)=x^2+2.x+2\\\implies g(-x)\neq g(x)$

∴ This shows it is not an even function.

Regarding the second function

$g(x)=2.x^2+1$

by replacing x with -x, we determine that

$g(-x)=2.(-x)^2+1\\g(-x)=2.x^2+1\\\implies g(-x)=g(x)$

∴ Hence, it qualifies as an even function.

For the third function

$g(x)=4.x+2$

by replacing x with -x, we obtain

$g(-x)=4.(-x)+2\\g(-x)=-4.x+2\\\implies g(-x)\neq g(x)$

∴ Thus, it is not an even function

For the fourth function

$g(x)=2.x$

when substituting x with -x, the result is

$g(-x)=2.(-x)\\g(-x)=-2.x\\\implies g(-x)\neq g(x)$

∴ Therefore, it is not an even function

As a result,only the second function qualifies as an even function.

You might be interested in

If f(x)=2x+1f(x)=2x+1f, left parenthesis, x, right parenthesis, equals, 2, x, plus, 1 and g(x)=x^2+7g(x)=x 2 +7g, left parenthes

Inessa [12570]

Answer:

The composite function;

f(g(x) = 2x^2 + 15

Step-by-step explanation:

Given f(x) = 2x + 1 and g(x) = x^2 + 7;

we are tasked with calculating f(g(x))

This represents a composite function where we substitute g(x) into f(x)

Consequently, we find

f(g(x)) = 2(x^2 + 7) + 1

f(g(x)) = 2x^2 + 14 + 1

f(g(x)) = 2x^2 + 15

5 0

3 months ago

Determine the value of base x if (211)x = (6A)16

AnnZ [12381]

This equation can be solved with two solutions, corresponding to $x=7$ and $x=-\dfrac{15}2$ .

4 0

2 months ago

Find the hcf by using long division method (219,1321,2320,8526)

babunello [11817]

Step-by-step explanation:

I included the work done

7 0

2 months ago

Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –

Zina [12379]

Answer:

The accurate representations are:

- 6x + 15 < 10 - 5x ⇒ 3rd option

A circle is open at 5 with a bold line extending right from 5 ⇒ 4th option (see diagram)

Step-by-step explanation:

Given the inequality is -3(2x - 5) < 5(2 - x)

First, simplify both sides:

∵ -3(2x - 5) = -3(2x) + -3(-5)

Remember that (-)(-) results in (+)

Thus, -3(2x - 5) = - 6x + 15

∵ 5(2 - x) = 5(2) + 5(-x)

Remember that (+)(-) results in (-)

Then, 5(2 - x) = 10 - 5x

Now we have: - 6x + 15 < 10 - 5x

Subtract 15 from both sides

So: - 6x < -5 - 5x

Add 5x to both sides

Thus, - x < - 5

Note that since the coefficient of x is negative, we reverse the inequality sign when dividing both sides by it

∵ The coefficient of x is -1

Therefore, dividing both sides by -1 gives us x > 5

The accurate representations are:

- 6x + 15 < 10 - 5x ⇒ 3rd option

A circle is open at 5 with a bold line extending right from 5 ⇒ 4th option (see diagram)

7 0

2 months ago

Read 2 more answers

Ava wants to figure out the average speed she is driving. She starts checking her car’s clock at mile marker 0. It takes her 4 m

Inessa [12570]

Answer:

45 mph

Step-by-step explanation:

Calculate the unit rate (i.e., speed):

6 mi 60 min

--------- * ------------- = (3/4)(60) mph = 45 mph

8 min 1 hr

6 0

2 months ago

Read 2 more answers