Question

in a sale room at a clothing store, every item is on sale for half its original price, plus $8. answer parts (a) through (d).
(b) write a function f that adds 8 to x.
f(x) = x + 8
(simplify your answer. use integers or fractions for any numbers in the expression.)
(c) write and simplify the function $(f \circ g)(x)$.
$(f \circ g)(x) = \frac{1}{2}x + 8$
(simplify your answer. use integers or fractions for any numbers in the expression.)
(d) use the function from part (c) to find the sale price of a shirt that has an original price of $58.
the sale price is $\square$.
(simplify your answer.)

Explanation:

Step1: Identify input value

Original price $x = 58$

Step2: Substitute into composite function

Substitute $x=58$ into $(f \circ g)(x) = \frac{1}{2}x + 8$
$\frac{1}{2}(58) + 8$

Step3: Calculate the result

First compute $\frac{1}{2}(58) = 29$, then $29 + 8 = 37$

Answer:

37