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professor190 [17]
3 years ago
7

Find two consecutive even integers such that the sum of the smaller and 3 times the larger is 330

Mathematics
1 answer:
tensa zangetsu [6.8K]3 years ago
4 0

Answer:

The 2 numbers = 81 and 83

Step-by-step explanation:

As, one number = x

The other, because it's an even number and consecutive = x + 2

So the larger numbef here is x + 2

And they are saying 3 times x + 2 plus x = 330

So let's solve!

3 times x + 2 = 3(x+2) = 3x + 6

So we will add it to x = (3x + 6) +(x) = 4x + 6

So they are saying the sum of them will be 330

So, 4x + 6 = 330

4x = 330 - 6

4x = 324

x = 324/4

x = 81

So x is the first number = 81

And the second is x + 2 = 81 + 2 = 83

So the 2 numbers are 81, 83

Lets check!

3 times the bigger number = 83 x 3 = 249

We will add it to 81 and we will get 330

So, 249 + 81 = 330

So the answer is right

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Given: f(x) = \frac{1}{x-2}

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A.)Consider

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f(\frac{2x+1}{x} )=\frac{1}{(\frac{2x+1}{x})-2}

f(\frac{2x+1}{x} )=\frac{1}{\frac{2x+1-2x}{x}}

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f(\frac{2x+1}{x} )=1

Also,

g(f(x))= g(\frac{1}{x-2} )

g(\frac{1}{x-2} )= \frac{2(\frac{1}{x-2}) +1 }{\frac{1}{x-2}}

g(\frac{1}{x-2} )= \frac{\frac{2+x-2}{x-2} }{\frac{1}{x-2}}

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Therefore, both functions are inverses of each other.


B.

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Since, the function f(g(x)) is not defined for x=0.

Therefore, the domain is (-\infty,0)\cup(0,\infty)


For the Composition function g(f(x)) =g(\frac{1}{x-2} )=x

Since, the function g(f(x)) is not defined for x=2.

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