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2 years ago

13

WILL MARK BRAINLIEST!!!!!!

2 answers:

11Alexandr11 [23.1K]2 years ago

3 0

F(x) = x^2 + 3
g(x) = sqrt(x - 2)

f(g(x)) = x - 2 + 3 = x + 1

joja [24]2 years ago

3 0

Answer:

The correct option is 3.

Step-by-step explanation:

The given functions are

$f(x)=x^2+3$

$g(x)=\sqrt{x-2}$

We need to find the value of f(g(x)).

$f(g(x))=f(\sqrt{x-2})$ $[\because f(x)=x^2+3]$ .... (1)

Substitute $x=\sqrt{x-2}$ in function f(x) to find the value of $f(\sqrt{x-2})$ .

$f(\sqrt{x-2})=(\sqrt{x-2})^2+3$

$f(\sqrt{x-2})=x-2+3$

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

Substitute the value of $f(\sqrt{x-2})$ in equation (1).

$f(g(x))=x+1$

Therefore, the correct option is 3.

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Prove that for all n in the naturals, n(n+1)(n+2) is divisible by 3

DerKrebs [107]

By induction:

It's true for $n=1$ , since $1\cdot2\cdot3$ clearly contains a factor of 3.

Suppose it's true for $n=k$ , that $k(k+1)(k+2)$ is divisible by 3. Then

$(k+1)(k+2)(k+3)=\dfrac{k(k+1)(k+2)(k+3)}k=\dfrac{3m(k+3)}k$

where $m$ is an integer. This reduces to

$\dfrac{3m(k+3)}k=3m+9\dfrac mk$

and both terms are clearly multiples of 3. We know that $\dfrac mk$ is an integer since we had set $m=k(k+1)(k+2)$ previously, which implies $m$ is a multiple of $k$ . So the statement is true.

6 0

2 years ago

If the difference of a number and two is tripled, the result is six more than the number. Find the number. Round your answer to

Nataly [62]

Answer:

6

Step-by-step explanation:

let the number be x

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2 years ago

A bus stops at the station near Kylie's house every 1 hours . Which expression could be used to find the number of times the bus

anastassius [24]

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5 0

2 years ago

The slope please. it must be one of the four options.

Mazyrski [523]

The answer to the question is a

3 0

3 years ago

If -2x+3=7 and 3x+1= 5+y

sertanlavr [38]

Answer: x = -2, y = -10

Step-by-step explanation:

solve for x first in the equation -2x+3=7

-2x+3=7

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now plug that x value into the other equation so we can find y

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7 0

2 years ago

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