Find the nth term of this quadratic sequence 2, 8, 18, 32, 50,

What is a two column proof

ruslelena [56]

A, the first choice. c doesn't say tht its in a logical flow

3 0

3 years ago

Read 2 more answers

If f(x) = x and g(x) = 2, what is (f o g)(x)? 2x 2 x + 2 x/2

arlik [135]

$(f \circ g)(x)=2$

8 0

3 years ago

Determine whether the statements are True or False. Justify your answer with an explanation.

frez [133]

Problem 1

<h3>Answer: False</h3>

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Explanation:

The notation (f o g)(x) means f( g(x) ). Here g(x) is the inner function.

So,

f(x) = x+1

f( g(x) ) = g(x) + 1 .... replace every x with g(x)

f( g(x) ) = 6x+1 ... plug in g(x) = 6x

(f o g)(x) = 6x+1

Now let's flip things around

g(x) = 6x

g( f(x) ) = 6*( f(x) ) .... replace every x with f(x)

g( f(x) ) = 6(x+1) .... plug in f(x) = x+1

g( f(x) ) = 6x+6

(g o f)(x) = 6x+6

This shows that (f o g)(x) = (g o f)(x) is a false equation for the given f(x) and g(x) functions.

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Problem 2

<h3>Answer: True</h3>

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Explanation:

Let's say that g(x) produced a number that wasn't in the domain of f(x). This would mean that f( g(x) ) would be undefined.

For example, let

f(x) = 1/(x+2)

g(x) = -2

The g(x) function will always produce the output -2 regardless of what the input x is. Feeding that -2 output into f(x) leads to 1/(x+2) = 1/(-2+2) = 1/0 which is undefined.

So it's important that the outputs of g(x) line up with the domain of f(x). Outputs of g(x) must be valid inputs of f(x).

7 0

3 years ago

Find the taylor polynomial t3(x) for the function f centered at the number

Vlad [161]

$e^{-3x}=\displaystyle\sum_{n=0}^\infty\frac{(-3x)^n}{n!}=1-3x+9x^2+\cdots$
$\sin2x=\displaystyle\sum_{n=0}^\infty\frac{(-1)^n(2x)^{2n+1}}{(2n+1)!}=2x-\dfrac{4x^3}3+\cdots$

$e^{-3x}\sin2x=\left(1-3x+9x^2+\cdots\right)\left(2x-\dfrac{4x^3}3+\cdots\right)$
$\approx T_3(x)=(1-3x+9x^2)\left(2x-\dfrac{4x^3}3\right)$
$T_3(x)=2x-6x^2+\left(18-\dfrac43\right)x^3$
$T_3(x)=2x-6x^2+\dfrac{50}3x^3$

5 0

3 years ago

Re-write the equation after you distribute and combine all the like terms. 12-4(-3x+5)-8x=20

dlinn [17]

Look at the attached picture ⤴

Hope it will help u...

3 0

3 years ago