Find the Inverse f(x)=2x^2-8x+1 , x>=2

Find the Inverse f(x)=2x^2-8x+1 , x>=2
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Find the range of the given function.
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The range is the set of all valid values. Use the graph to find the range.
Convert to an inequality.
Find the inverse.
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Interchange the variables.
Solve for .
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Rewrite the equation as .
Subtract from both sides of the equation.
Use the quadratic formula to find the solutions.
Substitute the values , , and into the quadratic formula and solve for .
Simplify.
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Simplify the numerator.
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Raise to the power of .
Multiply by .
Apply the distributive property.
Multiply by .
Multiply by .
Subtract from .
Factor out of .
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Factor out of .
Factor out of .
Rewrite as .
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Factor out of .
Rewrite as .
Add parentheses.
Pull terms out from under the radical.
Multiply by .
Simplify .
Simplify the expression to solve for the portion of the .
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Simplify the numerator.
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Raise to the power of .
Multiply by .
Apply the distributive property.
Multiply by .
Multiply by .
Subtract from .
Factor out of .
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Factor out of .
Factor out of .
Rewrite as .
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Factor out of .
Rewrite as .
Add parentheses.
Pull terms out from under the radical.
Multiply by .
Simplify .
Change the to .
Simplify the expression to solve for the portion of the .
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Simplify the numerator.
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Raise to the power of .
Multiply by .
Apply the distributive property.
Multiply by .
Multiply by .
Subtract from .
Factor out of .
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Factor out of .
Factor out of .
Rewrite as .
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Factor out of .
Rewrite as .
Add parentheses.
Pull terms out from under the radical.
Multiply by .
Simplify .
Change the to .
The final answer is the combination of both solutions.
Replace with to show the final answer.
Find the inverse using the domain and the range of the original function.
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Name

Name six hundred eleven million two hundred twenty-six thousand forty-five

Interesting facts

  • 611226045 has 16 divisors, whose sum is 1303948992
  • The reverse of 611226045 is 540622116
  • Previous prime number is 5

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 27
  • Digital Root 9

Name

Name one billion nine hundred ninety-five million six hundred fourteen thousand nine hundred seventy-eight

Interesting facts

  • 1995614978 has 8 divisors, whose sum is 3421054272
  • The reverse of 1995614978 is 8794165991
  • Previous prime number is 7

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 59
  • Digital Root 5

Name

Name one billion three hundred eighty-five million two hundred fifty-six thousand one hundred six

Interesting facts

  • 1385256106 has 8 divisors, whose sum is 2237721444
  • The reverse of 1385256106 is 6016525831
  • Previous prime number is 13

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 37
  • Digital Root 1