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13 days 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 [9K]13 days 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.

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If m<9=97° and m<12=114°, find each measure. I have to show my work.

Leona [9271]

Solution/Step-by-step breakdown:

Information provided:

m<9 = 97°

m<12 = 114°

a. m<1 = m<9 because they are corresponding angles, which are equal.

m<1 = 97° (using substitution)

b. m<2 + m<1 = 180° (since they form a linear pair)

m<2 + 97° = 180° (substitute the value)

m<2 = 180 - 97 (subtracting 97 from both sides)

m<2 = 83°

c. m<3 = m<11 (as they are corresponding angles)

m<11 + m<12 = 180° (linear pair)

m<11 + 114° = 180° (substituting the known angle)

m<11 = 180 - 114

m<11 = 66°

m<3 = m<11 = 66°

d. m<4 + m<3 = 180° (linear pair)

m<4 + 66° = 180° (substituting the known angle)

m<4 = 180 - 66

m<4 = 114°

e. m<5 = m<2 as vertical angles are equal.

m<5 = 83° (using substitution)

f. m<6 = m<1 (vertical angles are equal)

m<6 = 97° (using substitution)

g. m<7 = m<4 (as vertical angles are equal)

m<7 = 114° (using substitution)

h. m<8 = m<3 (due to vertical angles being equal)

m<8 = 66° (using substitution)

i. m<10 = m<2 (corresponding angles are equal)

m<10 = 83° (using substitution)

j. m<11 = m<3 (because they are vertical angles)

m<11 = 66° (using substitution)

k. m<13 = m<5 (corresponding angles)

m<13 = 83° (applying substitution)

l. m<14 = m<9 (as vertical angles)

m<14 = 97° (applying substitution)

m. m<15 = m<12 (as vertical angles)

m<15 = 114° (applying substitution)

n. m<16 = m<11 (because they are vertical angles)

m<16 = 66° (applying substitution)

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Step-by-step explanation:

What is a34 of the sequence 9,6,3,..

r=a2-a1

r=6-9

r=-3

a34=a1+33.r

a34=9+33.(-3)

a34= 9-99

a34= -90

hope this helps!

bye!

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