Question

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.​

Answer 1

All functions have an inverse expression.

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

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:

$\mathbf{C(x) = 50000 + (x - 100) \times 100}$

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

Expand

$\mathbf{C(x) = 50000 + 100x - 10000}$

Evaluate like terms

$\mathbf{C(x) = 40000 + 100x}$

To calculate the inverse function, we have:

$\mathbf{C(x) = 40000 + 100x}$

Replace C(x) with y

$\mathbf{y = 40000 + 100x}$

Swap x and y

$\mathbf{x = 40000 + 100y}$

Subtract 40000 from both sides

$\mathbf{x - 40000 = 100y}$

Divide both sides by 100

$\mathbf{\frac{x - 40000}{100} = y}$

Rewrite as:

$\mathbf{y= \frac{x - 40000}{100} }$

Split

$\mathbf{y= \frac{x}{100} - \frac{40000}{100} }$

$\mathbf{y= 0.01x - 400 }$

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

Read more about functions and inverse at:

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