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Charra [1.4K]
2 years ago
11

Sam says the longest ski trail is more than three times the length of the shortest ski trail. Eli says it is less than three tim

es the length. Who is correct? Explain.
Mathematics
1 answer:
iragen [17]2 years ago
6 0

Answer:

Sam

Step-by-step explanation:

Sam: Longest ski trail >3x    x = shortest ski trail

Eli: Longest ski train< 3x

Sam is correct because the longest ski trail has to be greater than the shortest and it can't be less than.

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Given that f(x) = x + 3<br> a) Find f(2)
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{ \qquad\qquad\huge\underline{{\sf Answer}}}

Here we go ~

In the above question, it is given that :

\qquad \sf  \boxed{ \sf f(x) =  \frac{x + 3}{2} }

A.) Find f(2) :

\qquad \sf  \dashrightarrow \: f(2) =  \dfrac{2 + 3}{2}

\qquad \sf  \dashrightarrow \: f(2) =  \dfrac{5}{2}

or

\qquad \sf  \dashrightarrow \: f(2) = 0.5

B.) Find { \sf {f}^{-1}(x) } :

\qquad \sf  \dashrightarrow \: let \: y = f (x)

so, we can write it as :

\qquad \sf  \dashrightarrow \: y =  \dfrac{x + 3}{2}

\qquad \sf  \dashrightarrow \: 2y = x + 3

\qquad \sf  \dashrightarrow \: x = 2y - 3

Now, put x = { \sf {f}^{-1}(x) }, and y = x and we will get our required inverse function ~

\qquad \sf  \dashrightarrow \: f {}^{ - 1}(x) = 2x- 3

C.) Find { \sf {f}^{-1}(12) } :

\qquad \sf  \dashrightarrow \: f {}^{ - 1}(12) = 2(12)- 3

\qquad \sf  \dashrightarrow \: f {}^{ - 1}(12) = 36- 3

\qquad \sf  \dashrightarrow \: f {}^{ - 1}(12) = 33

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