Algebra Answers

if a function is neither one-one nor onto , can we say it's a function? if yes , then which function. like this example f:A to B y=f(x)=x^2 +3 A={-1,1,2,3} B={4,5,6,7}
THIS IS NEITHER ONE-ONE NOR ONTO. SO , if it is a function, so what is the name of this ?

Why we use ≡ sign in decomposing a partial fraction ? like x/[(x-2)(x+1)] ≡ [A/(x-2)]+[B/(x+1)] and how we can say it's equivalent ?

Solve the following equation:
log7(x-1)^2 -log7(x+1) -log7(49) = 0

In purchasing food for a political rally, you erroneously order shucked medium-size Pacific oysters (which come 8 to 12 per U.S. pint) instead of shucked medium-size Atlantic oysters (which come 26 to 38 per U.S. pint). The filled oyster container shipped to you has the interior measure of 1.4 m x 17 cm x 26 cm, and a U.S. pint is equivalent to 0.4732 liter. By how many oysters is the order short of your anticipated count? Assume 10 oysters per pint for Pacific oysters and 32 oysters per pint for Atlantic oysters

You are to fix dinners for 440 people at a convention of Mexican food fans. Your recipe calls for 4 peppers per serving (one serving per person). However, you have only habanero peppers on hand. The spiciness of peppers is measured in terms of the scoville heat unit (SHU). On average, one pepper has a spiciness of 4000 SHU and one habanero pepper has a spiciness of 300000 SHU. To get the desired spiciness, how many habanero peppers should you substitute for the peppers in the recipe for the 440 dinners?

A tourist purchases a car in England and ships it home to the United States. The car sticker advertised that the car's fuel consumption was at the rate of 40 miles per gallon on the open road. The tourist does not realize that the U.K. gallon differs from the U.S. gallon:

1 U.K. gallon = 4.545 963 1 liters
1 U.S. gallon = 3.785 306 0 liters

For a trip of 780 miles (in the United States), how many gallons of fuel does (a) the mistaken tourist believe she needs and (b) the car actually require?

On a spending spree in Malaysia, you buy an ox with a weight of 28.5 piculs in the local unit of weights: 1 picul = 100 gins, 1 gin = 16 tahils, 1 tahil = 10 chees, and 1 chee = 10 hoons. The weight of 1 hoon corresponds to a mass of 0.3779 g. When you arrange to ship the ox home to your astonished family, how much mass must you declare on the shipping manifest?

-1≤x≤0 does the following equation x= - sqrt (1-y^2) satisfies the above condition?
i think it should be x= ±sqrt (1-y^2)for this condition

x 7/16 - x 5/16 + x 1/2

if f(x1)=f(x2) then x1=x2 then it's an injective function or x1 is not equal to x2 then f(x1) is not equal to f(x2) then it's also injective.

is it necessary to abide both the rules to be injective or any one?