A store has issued two different coupons for its customers to use. One coupon gives customers $$20$ off their purchase price, and the other coupon gives customers $35\%$ off of their purchase. The store allows customers to use both coupons and choose which coupon to apply first. For this context, ignore sales tax.

Let $f$ be the function that inputs a cost $($in dollars$)$ and outputs the cost after applying the $"$ $$20$ off" coupon, and let $g$ be the function that inputs a cost $($in dollars$)$ and outputs the cost after applying the $"35\%$ off" coupon.

a$.$ A customer purchases an item for $$100$ and asks the cashier to apply the $"$ $$20$ off" coupon first, followed by the $"35\%$ off" coupon. What is the cost of the item after the two coupons are applied?

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b$.$ A customer purchases an item for $$100$ and asks the cashier to apply the $"$ $$20$ off" coupon first, followed by the $"35\%$ off" coupon. Use function notation to represent the cost of the item $($in dollars$)$ after the two coupons are applied.

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c$.$ A customer purchases an item for $$100$ and asks the cashier to apply the $"35\%$ off" coupon first, followed by the $"$ $$20$ off" coupon. What is the cost of the item after the two coupons are applied?

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d$.$ A customer purchases an item for $$100$ and asks the cashier to apply the $"35\%$ off" coupon first, followed by the $"$ $$20$ off" coupon. Use function notation to represent the cost of the item $($in dollars$)$ after the two coupons are applied.

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