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You are planning to give you're a regale birthday surprise this coming 12 of July as she about to celebrate her 50th birthday. The Venue 88 as place to where the celebration will be held offers you a deal for the venue cost with a base fare of 50,000 pesos plus 100 per guest in excess of 100 guest and your budget for venue expenses is limited only to 150,000.

1. State cost as a function of number of guest.
2. Determine the expression for the inverse.​

Respuesta :

MrRoyal

All functions have an inverse expression.

  • The cost function is: [tex]\mathbf{C(x) = 40000 + 100x}[/tex].
  • The inverse function is: [tex]\mathbf{C'(x) = 0.01x - 400 }[/tex]

From the question, we have the following observations:

  • Base fare = 50000 pesos for first 100
  • Additional guest = 100 pesos

So, the cost function would be:

[tex]\mathbf{C(x) = 50000 + (x - 100) \times 100}[/tex]

Where: x represents the number of guests, and C(x) represents the cost function

Expand

[tex]\mathbf{C(x) = 50000 + 100x - 10000}[/tex]

Evaluate like terms

[tex]\mathbf{C(x) = 40000 + 100x}[/tex]

To calculate the inverse function, we have:

[tex]\mathbf{C(x) = 40000 + 100x}[/tex]

Replace C(x) with y

[tex]\mathbf{y = 40000 + 100x}[/tex]

Swap x and y

[tex]\mathbf{x = 40000 + 100y}[/tex]

Subtract 40000 from both sides

[tex]\mathbf{x - 40000 = 100y}[/tex]

Divide both sides by 100

[tex]\mathbf{\frac{x - 40000}{100} = y}[/tex]

Rewrite as:

[tex]\mathbf{y= \frac{x - 40000}{100} }[/tex]

Split

[tex]\mathbf{y= \frac{x}{100} - \frac{40000}{100} }[/tex]

[tex]\mathbf{y= 0.01x - 400 }[/tex]

Hence, the inverse function is: [tex]\mathbf{C'(x) = 0.01x - 400 }[/tex]

Read more about functions and inverse at:

https://brainly.com/question/10300045

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