is g(x)=2x^2-1 bijective? explain with reasons
Answers
Step-by-step explanation:
The Qulliq, a type of oil lamp made by the arctic peoples, are also known as soapstone lamps. This kind of lamp was the single most important article of furniture for the Inuit peoples in their dwellings.
Ancient Egyptian Scarab signet/amulets were most commonly made from glazed steatite.[5]
Soapstone is used for inlaid designs, sculpture, coasters, and kitchen countertops and sinks. The Inuit often used soapstone for traditional carvings. Some Native American tribes and bands make bowls, cooking slabs, and other objects from soapstone; historically, this was particularly common during the Late Archaic archaeological period.[6]
Locally quarried soapstone was used for gravemarkers in 19th century northeast Georgia, US, around Dahlonega, and Cleveland, as simple field stone and "slot and tab" tombs.
Small blocks of soapstone (8" x 10" x 1") were heated on the cookstove or near the fire and used to warm cold bedclothes or to keep hands and feet cozy while sleighing.
Soapstone is relatively abundant in northern Europe. Vikings hewed soapstone directly from the stone face, shaped it into cooking pots, and sold these at home and abroad.[7] In Shetland, there is evidence these vessels were used for processing marine and dairy fats.[8] Several medieval buildings have survived here which are constructed with soapstone, amongst them Nidaros Cathedral.[3]
Soapstone is sometimes used for construction of fireplace surrounds, cladding on wood-burning stoves,[9][10] and as the preferred material for woodburning masonry heaters because it can absorb, store, and evenly radiate heat due to its high density and magnesite (MgCO3) content. It is also used for countertops and bathroom tiling because of the ease of working the material and its property as the "quiet stone". A weathered or aged appearance occurs naturally over time as the patina is enhanced.
The ancient trading city of Tepe Yahya in southeastern Iran was a center for the production and distribution of soapstone in the fifth to third millennia BC.[11] It was also used in Minoan Crete. At the Palace of Knossos, archaeological recovery has included a magnificent libation table made of steatite.[12] The Yoruba people of West Nigeria used soapstone for several statues, most notably at Esie, where archaeologists have uncovered hundreds of male and female statues about half of life size. The Yoruba of Ife also produced a miniature soapstone obelisk with metal studs called "the staff of
Answer:
Given, function f:R→R such that f(x)=1+x2,
Let A and B be two sets of real numbers.
Let x1,x2∈A such that f(x1)=f(x2).
⇒1+x12=1+x22⇒x12−x22=0⇒(x1−x2)(x1+x2)=0
⇒x1=±x2. Thus f(x1)=f(x2) does not imply that x1=x2.
For instance, f(1)=f(−1)=2, i.e. , two elements (1, -1) of A have the same image in B. So, f is many-one function.
Now, y=1+x2⇒x=y−1⇒elements < y have no pre-image in A (for instance an element -2 in the codomain has no pre-image in the domain A). So, f is not onto.
Hence, f is neither one-one onto. So, it is not bijective