Answer:
f−1(f(x)) = f(f−1(x)) = x
Step-by-step explanation:
Follow this simple example using the function f(x) = x + 2
f(x) = x + 2
NOw we find the inverse function f^(1)(x).
y = x + 2
x = y + 2
y = x - 2
f^(-1)(x) = x - 2
The inverse function is f^(-1)(x) = x - 2
Now we do the two compositions of functions:
f^(-1)(f(x)) = x + 2 - 2 = x
f(f^(-1)(x)) = x - 2 + 2 = x
Both are equal to x.
Answer: f−1(f(x)) = f(f−1(x)) = x
Answer:
66 2/3 mL
Step-by-step explanation:
Let v represent the volume in mL of added 30% solution. Then the amount of salt in the mix is ...
0.10×100 +0.30×v = 0.18(100 +v)
0.12v = 0.08(100) . . . . .subtract (0.18v +0.10×100)
v = 8/0.12 . . . . . . . . . . . divide by the coefficient of v
v = 66 2/3 . . . . mL
Adding 66 2/3 mL of 30% salt solution to 100 mL of 10% salt solution will make 166 2/3 mL of 18% salt solution.
Answer:
5,418.2 feet
Step-by-step explanation:
Nadia is carrying out mountain climbing.
She started climbing the mountain at an altitude of 19.26 feet below the sea level.
Nadia changed her altitude by climbing a total of 5,437.8 feet from her starting position.
Therefore, Nadia's altitude at the end of her climb can be calculated as follows
= 5,437.8-19.6
= 5,418.2
Hence Maria's altitude at the end of her climb is 5,418.2 feet
Answer:
Total number of required ways = 12 × 51!
Step-by-step explanation:
Number of total cards in the deck = 52
Number of face cards in the deck = 12
Now, we need to find the number of ways such that the first card is always a face card
Now, first card is face card so number of cards left to be arranged = 52 - 1 = 51
Number of ways to arrange 51 cards = 51!
Also, Number of face cards = 12
So, Total number of required ways = 12 × 51!