Problem StatementAlice wants to balance her time spent playinggames and studying. She only likes to playgames that are either action or adventuregames or both.Alice has a collection of N games. The genres ofthese games are categorized by Alice as follows:• 0 - neither action nor adventure. 1 - action• 2 - adventure3- both action and adventureYou are given the genres of games Alice hasalong with the time required to finish each ofthem. Alice wants to play at-least M games ofaction and M games of adventure in the leastamount of time so she can give the rest of thetime to her studies.You're being proctored!Your task is to determine thetime in which Alice can meetquota Print -1 if it is not possiSelect languagePython 3
Answers
Answer:
f(x)=
log
10
(
4
5x−x²
)
Separate the function into parts to determine the domain of each part.
\to \sqrt {\log_{10}\left(\dfrac{5x-x²}{4}\right) }→
log
10
(
4
5x−x²
)
\to \log_{10}\left(\dfrac{5x-x²}{4}\right)→log
10
(
4
5x−x²
)
\to 5x-x²→5x−x²
Let's solve one by one.
\to \sqrt {log_{10}\left(\dfrac{5x-x²}{4}\right) }→
log
10
(
4
5x−x²
)
The domain of an even root function are all values of x for which the radicand is positive or 0.
\sqrt {\log_{10}\left(\dfrac{5x-x²}{4}\right) }=0
log
10
(
4
5x−x²
)
=0
\log_{10}\left(\dfrac{5x-x²}{4}\right) =0log
10
(
4
5x−x²
)=0
\dfrac{5x-x²}{4}=1
4
5x−x²
=1
5x-x²=45x−x²=4
5x-x²-4=05x−x²−4=0
-x²+5x-4=0−x²+5x−4=0
x²-5x+4=0x²−5x+4=0
x²-x-4x+4=0x²−x−4x+4=0
x(x-1)-4(x-1)=0x(x−1)−4(x−1)=0
(x-1)(x-4)=0(x−1)(x−4)=0
x=1\:and\:x=4x=1andx=4
x\in [1,4]x∈[1,4]
\to \log_{10}\left(\dfrac{5x-x²}{4}\right)→log
10
(
4
5x−x²
)
The domain of a logarithmic function are all values of x for which the argument is positive.
x\in [0,5]x∈[0,5]
\to 5x-x²→5x−x²
The domain of a quadratic function is the set of all real numbers.
x\in Rx∈R
Now, we have to find the intersection.
x\in [1,4]x∈[1,4]