Question

function c is defined by the equation d(n) = 50 + 4n. it gives the monthly cost, in dollars, of visiting a gym as a function of the number of visits, n.
part a
find the inverse function.
type the answer in the box below.

part b
find the value of d(7).
type the answer in the box below.

Explanation:

Part A

Step1: Replace \( d(n) \) with \( y \)

\( y = 50 + 4n \)

Step2: Swap \( n \) and \( y \)

\( n = 50 + 4y \)

Step3: Solve for \( y \)

Subtract 50 from both sides: \( n - 50 = 4y \)
Divide both sides by 4: \( y = \frac{n - 50}{4} \)
Rewrite \( y \) as \( d^{-1}(n) \)
\( d^{-1}(n) = \frac{n - 50}{4} \)

Step1: Substitute \( n = 7 \) into \( d(n) = 50 + 4n \)

\( d(7) = 50 + 4\times7 \)

Step2: Calculate the multiplication

\( 4\times7 = 28 \)

Step3: Calculate the addition

\( 50 + 28 = 78 \)

Answer:

\( d^{-1}(n) = \frac{n - 50}{4} \)

Part B