Answer:
- The function is injective but nor surjective
Step-by-step explanation:
<u>We see that:</u>
<u>For any x₁ and x₂ ∈ N, </u>
- f(x) = x₁³ = x₂³ ⇒ x₁ = x₂, both are natural numbers
It it confirmed one-to-one, hence it is injective
<u>Check the surjectivity:</u>
f(x) = y ∈ N
<u>Let y = 2, then:</u>
Since x is not natural, the function is not surjective
A coplanar point are points that lie on the same line. An angle is the intersection of two noncollinear rays at a common endpoint. The rays are called sides and the common endpoint is called the vertex.
hope that helps
X^3 = 216
by taking cubic root for both sides
![\sqrt[3]{x^3} = \sqrt[3]{216}](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7Bx%5E3%7D%20%3D%20%20%5Csqrt%5B3%5D%7B216%7D%20)
x = 6
Answer:
B and C
Step-by-step explanation:
Rearrange each equation into slope- intercept form
A
3x - 2y = 4 ( subtract 3x from both sides )
- 2y = - 3x + 4 ( divide all terms by - 2 )
y =
x - 2 ← not equivalent
B
2x - 3y = 12 ( subtract 2x from both sides )
- 3y = - 2x + 12 ( divide all terms by - 2 )
y =
x - 4 ← equivalent
C
- 4(2x - 3y ) = - 48 ( divide both sides by - 4 )
2x - 3y = 12 ← same as B ⇒ equivalent
D
2(x + 6) = 3y
3y = 2x + 12 ( divide all terms by 3 )
y =
x + 4 ← not equivalent
E
2x - 3y = 4 ( subtract 2x from both sides )
- 3y = - 2x + 4 ( divide all terms by - 3 )
y =
x -
← not equivalent
Answer:
The answer is below
Step-by-step explanation:
The horizontal asymptote of a function f(x) is gotten by finding the limit as x ⇒ ∞ or x ⇒ -∞. If the limit gives you a finite value, then your asymptote is at that point.
![\lim_{x \to \infty} f(x)=A\\\\or\\\\ \lim_{x \to -\infty} f(x)=A\\\\where\ A\ is\ a\ finite\ value.\\\\Given\ that \ f(x) =25000(1+0.025)^x\\\\ \lim_{x \to \infty} f(x)= \lim_{x \to \infty} [25000(1+0.025)^x]= \lim_{x \to \infty} [25000(1.025)^x]\\=25000 \lim_{x \to \infty} [(1.025)^x]=25000(\infty)=\infty\\\\ \lim_{x \to -\infty} f(x)= \lim_{x \to -\infty} [25000(1+0.025)^x]= \lim_{x \to -\infty} [25000(1.025)^x]\\=25000 \lim_{x \to -\infty} [(1.025)^x]=25000(0)=0\\\\](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20f%28x%29%3DA%5C%5C%5C%5Cor%5C%5C%5C%5C%20%5Clim_%7Bx%20%5Cto%20-%5Cinfty%7D%20f%28x%29%3DA%5C%5C%5C%5Cwhere%5C%20A%5C%20is%5C%20a%5C%20finite%5C%20value.%5C%5C%5C%5CGiven%5C%20that%20%5C%20f%28x%29%20%3D25000%281%2B0.025%29%5Ex%5C%5C%5C%5C%20%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20f%28x%29%3D%20%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20%5B25000%281%2B0.025%29%5Ex%5D%3D%20%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20%5B25000%281.025%29%5Ex%5D%5C%5C%3D25000%20%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20%5B%281.025%29%5Ex%5D%3D25000%28%5Cinfty%29%3D%5Cinfty%5C%5C%5C%5C%20%5Clim_%7Bx%20%5Cto%20-%5Cinfty%7D%20f%28x%29%3D%20%5Clim_%7Bx%20%5Cto%20-%5Cinfty%7D%20%5B25000%281%2B0.025%29%5Ex%5D%3D%20%5Clim_%7Bx%20%5Cto%20-%5Cinfty%7D%20%5B25000%281.025%29%5Ex%5D%5C%5C%3D25000%20%5Clim_%7Bx%20%5Cto%20-%5Cinfty%7D%20%5B%281.025%29%5Ex%5D%3D25000%280%29%3D0%5C%5C%5C%5C)
