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ololo11 [35]
2 years ago
7

Find the inverse of the function

Mathematics
1 answer:
lozanna [386]2 years ago
4 0

as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.

\stackrel{h(x)}{y}~~ = ~~6\sqrt[3]{2x+5}-1\implies \stackrel{\textit{quick switcheroo}}{x~~ = ~~6\sqrt[3]{2y+5}-1} \\\\\\ x+1=6\sqrt[3]{2y+5}\implies \cfrac{x+1}{6}=\sqrt[3]{2y+5}\implies \left( \cfrac{x+1}{6} \right)^3=\left( \sqrt[3]{2y+5} \right)^3

\left( \cfrac{x+1}{6} \right)^3=2y+5\implies \left( \cfrac{x+1}{6} \right)^3-5=2y\implies \cfrac{\left( \frac{x+1}{6} \right)^3-5}{2}=y \\\\\\ \cfrac{\left( \frac{x+1}{6} \right)^3}{2}-\cfrac{5}{2}=y\implies \cfrac{~~ \frac{(x+1)^3}{6^3}~~}{2}-\cfrac{5}{2}=y\implies \cfrac{(x+1)^3}{432}-\cfrac{5}{2}=\stackrel{y}{h^{-1}(x)}

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What is the Inverse Equation<br><br>f(x) =6x-1 ?? please I need help!​
Scrat [10]

Answer:

f^{-1}(x)=\frac{x+1}{6}

Step-by-step explanation:

So we have the function:

f(x)=6x-1

To find the inverse function, switch x and f(x), change f(x) to f⁻¹(x), and solve for f⁻¹(x). Therefore:

f(x)=6x-1

Switch:

x=6f^{-1}(x)-1

Add 1 to both sides:

x+1=6f^{-1}(x)

Divide both sides by 6:

f^{-1}(x)=\frac{x+1}{6}

And that's our answer :)

5 0
3 years ago
Prove x²+y² = (x+y) (x-y)​
gtnhenbr [62]

Answer:

(x+y)(x-y)

x^2 - xy + xy - y^2

x^2 - y^2

7 0
2 years ago
Trina planted plants in her garden last week. She planted twice as many cucumbers as zucchini and eight more tomatoes than cucum
maxonik [38]

Answer:

7 Zuchini, 14 Cucumbers and 22 Tomatoes plants.

Step-by-step explanation:

  • Let the number of tomatoes=t
  • Let the number of cucumber planted=c
  • Let the number of zucchini planted=z
  • Total Number of Plants=43

She planted twice as many cucumbers as zucchini, this is written as:

  • c=2z

She also planted eight more tomatoes than cucumbers, this is written as:

  • t=c+8=2z+8

In total, she planted 43 plants

Therefore:

z+(2z)+(2z+8)=43

5z+8=43

5z=43-8

5z=35

Divide both sides by 5

z=7

Number of Cucumbers, c=2z=2 X 7 =14

Number of Tomatoes, t=c+8=14+8=22

Therefore, she planted 7 Zuchini, 14 Cucumbers and 22 Tomatoes plants.

3 0
3 years ago
the equation of the line is y=17.63x+27.52. What is the best interpretation of the y-intercept of the line?
baherus [9]

Answer:

jfskdkgfkd the him to Southwest flight and hotel and the him her i is not available I i the Himalayan region and dad ❣️❤️❣️ the him to all religions are going well for tiles wall Street actress and singer and songwriter producer of natural resources and plane and the

3 0
3 years ago
Milan rented a truck for one day. There was a base fee of $20.99, and there was an additional charge of 74 cents for each mile d
malfutka [58]

Answer:

m = 134 miles

Step-by-step explanation:

f(m) = 16.95 + 0.92m

140.23 = 16.95 + 0.92m

0.92m = 140.23 - 16.95

0.92m = 123.28

m = 123.28/0.92

m = 134 miles

4 0
3 years ago
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