If $h(x)=6-x$, what is the value of $(h \circ h)(10)?

First, find h ( 10 ) by substituting x = 10 into h ( x ) = 6 − x , which gives h ( 10 ) = 6 − 10 = − 4 .
Then, find h ( h ( 10 )) by substituting h ( 10 ) = − 4 into h ( x ) , which gives h ( − 4 ) = 6 − ( − 4 ) = 10 .
Therefore, ( h c i rc h ) ( 10 ) = 10 .
The final answer is 10 ​ .

Explanation

Understanding the Problem We are given the function h ( x ) = 6 − x , and we want to find the value of ( h c i rc h ) ( 10 ) , which means h ( h ( 10 )) . This is a composition of functions, where we first evaluate the inner function h ( 10 ) , and then we use that result as the input for the outer function h ( x ) .

Evaluating h(10) First, we evaluate h ( 10 ) . We substitute x = 10 into the expression for h ( x ) : h ( 10 ) = 6 − 10 = − 4.

Evaluating h(h(10)) Next, we evaluate h ( h ( 10 )) , which is h ( − 4 ) . We substitute x = − 4 into the expression for h ( x ) : h ( − 4 ) = 6 − ( − 4 ) = 6 + 4 = 10.

Final Answer Therefore, ( h c i rc h ) ( 10 ) = 10 .


Examples
Composite functions are useful in many real-world scenarios. For example, consider a store that offers a discount on an item and then applies sales tax. If d ( x ) represents the price after the discount and t ( x ) represents the price after sales tax, then ( t c i rc d ) ( x ) represents the final price you pay. Understanding composite functions helps you analyze such situations and predict outcomes.

Answered by GinnyAnswer | 2025-07-03

To find ( h ∘ h ) ( 10 ) , we first calculate h ( 10 ) = − 4 and then h ( − 4 ) = 10 . Therefore, the final answer is 10 .
;

Answered by Anonymous | 2025-07-04