Mathematics, 29.01.2020 00:51 ari758540

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

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An even function can be reflected about the y axis and map onto itself
example: y=x^2

an odd function can be reflected about the origin and map onto itself
example: y=x^3

a simple test is the following

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

so

even function
subsitute -x for each and see if we get the same function
remember to fully expand these

g(x)=(x-1)^2+1=x^2-2x+1+1=x^2-2x+2 is the original one

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 same because the original has -2x
not even

g(x)=2x^2+1
g(-x)=2(-x)^2+1
g(-x)=2x^2+1
same, it's even

g(x)=4x+2
g(-x)=4(-x)+2
g(-x)=-4x+2
not the same, not even

g(x)=2x
g(-x)=2(-x)
g(-x)=-2x
not same, not even

g(x)=2x²+1 is the even function

Answer from: jm900643

2nd function is even function.

Step-by-step explanation:

Given Functions 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 are functions whose value didnt change if we replace the variable with negative of the variable.i.e., f(x) = f(-x)

here,

1st function

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

replacing x by -x we get

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

∴ It is not an even function.

2nd function

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

replacing x by -x we get,

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

∴It is an even function.

3rd function

g(x)=4.x+2

replacing x by -x we get,

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

∴It is not an even function

4th function

g(x)=2.x

replacing x by -x we get,

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

∴It is not an even function

Therefore, only 2nd function is even function.

Answer from: Quest

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be). so point b is at (-2,2). point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3

Answer from: Quest

Answer is a not really sure tho

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

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