Each shelf was 1/10 of a yard long.
<h3>What are Arithmetic operations?</h3>
Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.
<h3>What is the fraction?</h3>
A fraction is defined as a numerical representation of a part of a whole that represents a rational number.
Given that Luca cut 5 shelves of equal length using 1/2 of a yard of wood
There were 5 shelves.
1/2 divided by 5
⇒ (1/2)/5
⇒ (1/2)/(5/1)
⇒ (1/2)(1/5)
⇒ 1/10
Hence, each shelf was 1/10 of a yard long.
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The given function is even.
Solution:
<em>If f(-x) = f(x), then the function is even.</em>
<em>If f(-x) = -f(x), then the function is odd.</em>
Given function:
Substitute x = -x
= f(x) (given)
f(-x) = f(x)
From the definition, it is even.
Hence the given function is even.
Inverse functions are usually denoted as g(x) and h(x), where g(x) is the original equation and h(x) is the corresponding inverse function. You can determine if the equations are inverse of each other if a certain point (a,b) on g(x) is on h(x) as point (b,a). So, there is a pattern wherein the x and y coordinates interchange with each other. Also, you could see it visually when you graph both equations. They are mirror images of each other about line y=x or a 45° line.
One way to solve if the equations are inverse of each other is if they meet this condition:
g( h(x) ) = h( g(x) )
Suppose g(x) = 3x + 7. To find its inverse, change g(x) to y first so as not to confuse you:
y = 3x + 7
Next, interchange y and x variables
x = 3y + 7
Isolate y on one side and x on the other:
y = (x - 7)/3 = h(x)
That is the inverse equation for g(x) denoted as h(x). To check, let's verify the condition:
g((x - 7)/3) = h(3x + 7)
3(x - 7)/3) + 7 ? ((3x + 7 - 7)/3
x - 7 + 7 ? 3x/3
x = x
Therefore, g(x) and h(x) are indeed inverse functions of each other.
Answer:
B and D
Step-by-step explanation:
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