Answer:
18pi
Step-by-step explanation:
Let's take a look at the <em>relationship</em> between x and y in this function. When we look at the first non-zero pair, (-1, 1), we can see that, in the transition from x to y, our x value was had to have been multiplied by -1. For now, we could tentatively say that y = -x. Unfortunately, the next pair, (-4, 2), debunks this hypothesis pretty quickly, as 2 ≠ -(-4). We'll need to reexamine the relationship between x and y here.
One patter that we can be fairly confident in is that multiplication by -1; the sign is flipped from negative to positive when we go from x to y in each case, so we can hold onto that component of the function. Something else is happening before that sign flip, though, and we'll need to look into that by seeing how else the numbers are connected.
Ignoring the negative signs for a moment, let's take a look at the pairs (1,1) and (4, 2). We can transform 1 to 1 pretty easily; we simply multiply or divide it by 1. From 4 to 2, we can either divide it by 2 or multiply it by 1/2. Let's thing in terms of division for now. We know that
1/1 = 1 (obviously)
4/2 = 2
We might have something here! It looks like the number we divide by and the number we obtain are the same, so let's explore this further. Multiplying both sides by those denominators, we find:
1 = 1²
4 = 2²
Almost there! To finally find the relationship, we just square root both sides to get:
√1 = 1
√4 = 2
So that was the function we'd been looking for - a square root! Putting that together with what we said about changing the sign at the beginning, we have:
y =√(-x)
To verify this, we just need to plug in a few pairs, and we find that indeed:
1 = √-(-1) = √1 = 1
2 = √-(-4) = √4 = 2
Step-by-step explanation:
Wages
£450
450 x 1.02 = 459
Rent
£200
200 x 1.05 = 210
wages increases by £9
rent increases by £10
No the increase in her wages will not fully pay for the increase in the rent
Answer:
g(f(x) = 12x^2-2
Step-by-step explanation:
solution:
given,
f(x)=3x^2-1
g(x)=4x+2
g(f(x)=?
here,
g(f(x) = g(3x^2-1) [put the value of f(x) given]
=4(3x^2-1)+2 [ now put the value of g(x) and in the place of x put 3x^2-1]
=12x^2-4+2 [ by multiplying 4(3x^2-1) ]
= 12x^2-2 ans..
So g(f(x)=12x^2-2
hope its helps , I tried my best to explain there
hope you understand it as i am terrible at explaining like this ...
have a good time(•‿•)
Answer:
the first and second option
Step-by-step explanation:
