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2 years ago

What kind of graph is shown below?

Mathematics

1 answer:

Lemur [1.5K]2 years ago

6 0

Answer:

Step-by-step explanation:

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F(x) = 3x-1 , (f of g)(x) = x^2 , Find g(x)

fomenos

Answer:

$g(x)=\dfrac{x^2+1}{3}$

Step-by-step explanation:

Given functions:

$\begin{cases}f(x)=3x-1\\(f \circ g)(x)=x^2\end{cases}$

Composite functions are when the output of one function is used as the input of another.

Therefore, the given composite function (f o g)(x) means to substitute function g(x) in place of the x in function f(x).

$\begin{aligned}(f \circ g)(x) & = x^2\\f(g(x)) & = x^2\\\implies 3(g(x))-1 & = x^2\\3(g(x))-1+1 & = x^2+1\\3(g(x))&=x^2+1\\\dfrac{3(g(x))}{3}&=\dfrac{x^2+1}{3}\\\implies g(x)&=\dfrac{x^2+1}{3}\end{aligned}$

Therefore:

$\boxed{g(x)=\dfrac{x^2+1}{3}}$

6 0

8 months ago

75 points. Will give certified if work is shown and the answer is correct.

Svetach [21]

Volume of the first dwarf planet (r₁ = 832 mi):

$V_1=\dfrac{4}{3}\cdot\pi\cdot r_1^3=\dfrac{4}{3}\cdot\pi\cdot 832^3=\dfrac{2303721472}{3}\pi\approx7.679\cdot10^8\pi\,\text{mi}^3$

Volume of the second dwarf planet (r₂ = 829 mi):

$V_2=\dfrac{4}{3}\cdot\pi\cdot r_2^3=\dfrac{4}{3}\cdot\pi\cdot 829^3=\dfrac{2278891156}{3}\pi\approx7.5963\cdot10^8\pi\,\text{mi}^3$

So difference between the volumes is:

$V_1-V_2\approx7.679\cdot10^8\pi-7.5963\cdot10^8\pi=0.0827\cdot10^8\pi=\boxed{8270000\pi\,\text{mi}^3}$

or if we want exact value (we use (a³-b³) = (a-b)(a²+ab+b²) ):

$V_1-V_2=\dfrac{4}{3}\cdot\pi\cdot r_1^3-\dfrac{4}{3}\cdot\pi\cdot r_2^3=\dfrac{4}{3}\pi(r_1^3-r_2^3)=\dfrac{4}{3}\pi(832^3-829^3)=\\\\\\=\dfrac{4}{3}\pi(832-829)(832^2+832\cdot829+829^2)=\\\\\\=\dfrac{4}{3}\pi\cdot3(692224+689728+687241)=4\pi\cdot2069193=\boxed{8276772\pi\,\text{mi}^3}$

3 0

2 years ago

For which values of P and Q does the following equation have infinitely many solutions ?

Rzqust [24]

I’d say the answer would be d

7 0

3 years ago

He values in the table represent a linear function. How does the value of y change in relation to a change in the value of x?

Ivahew [28]

Answer:

Step-by-step explanation:

because I have did this at school

7 0

2 years ago

Evaluate (c − b)2 + a2 for a = –5, b = –2, and c = –4.

taurus [48]

(c - b)² + a²

a = -5

b = -2

c = -4

(-4 - (-2))² + (-5)²

(-4 + 2)² + (-5)²

(-2)² + (-5)²

4 + 25

3 0

3 years ago