Answer:
A function
Step-by-step explanation:
This is the exact definition of what makes a function.
Examples of functions are
lines: like the equation y = 3x
what ever value you plug in for x, it results in only one value for y
Quadratics: like the equation y = x²
what ever value you plug in for x, it results in only one value for y
The way we approach a problem like this is by using a technique called "collecting like terms".
This means that we want to put all of the values with an "x" on one side and all of the normal numbers on the other. For this particular problem we can do this as follows:
5x - 6 = x + 12
Now move the (- 6) to the right side of the equation by adding 6 to both sides:
=> 5x = x + 12 + 6
Now move the (x) to the left side of the equation by subtracting (x) from both sides:
=> 5x - x = 12 + 6
Now perform the simple arithmetic on both sides:
=> 4x = 18
Now remove the 4 from in front of the (x) by multiplying the whole equation by (1/4)
=> x = 18/4
Therefore to make your open sentence true, x must equal 18/4, or to simplify, 9/2, or as a decimal, 4.5. I hope this helped, and remember to try and understand not just the answer, but the maths involved in getting to the answer too :))
Answer:
Option B and C are correct.
Step-by-step explanation:
Inverse function: If both the domain and the range are R for a function f(x), and if f(x) has an inverse g(x) then:
for every x∈R.
Let and
Use logarithmic rules:
then, by definition;
=
Similarly;
for and
then, by definition;
=
Similarly,
g(f(x)) = x
Therefore, the only option B and C are correct. As the pairs of functions are inverse function.
Which of the following is a geometric sequence? 3, 6, 12, 24, … 4, 8, 12, 16, … 2, 4, 16, 256, …
Svetlanka [38]
Answer:
The geometric sequence would be 3, 6, 12, 24 . . .
Step-by-step explanation:
A <u>geometric sequence</u> is when the you find the next term in the sequence by multiplying by a <em>common ratio</em>. (A common ratio is the constant value that you <em>multiply</em> by each time in a geometric sequence.) In order to solve your problem, you would find the relationship between each term in the sequence. For the first sequence, 3, 6, 12, 24, etc., you can see that the ratio between one term and the next would be two: 3×2 = 6, 6×2 = 12, 12×2 = 24, and so on. This makes it a geometric sequence, but you still need to check the other sequences to make sure. For the sequence 4, 8, 12, 16, . . . , you need to add four each time. This means that the sequence has a <em>common difference</em>, or the constant value you <em>add or subtract</em> by in an <u>arithmetic sequence</u>. So, we know that the second sequence is not the answer. Finally, we check the last sequence, and if you look at it you can see that the you square the previous term to get the current one. This is different from a geometric sequence, and has a different name. However, it is not a geometric sequence because you are not multiplying by the <em>same</em> value each time (it doesn't have a common ratio). So, the first sequence, 3, 6, 12, 24, . . . , is a geometric sequence.