Question

if f: a-->b be defined by y = f(x) =x^2-2 and same function defined in the set of ordered pair form is {(2,....),(3,..),(.....,14)(....,-1), find the missing components of the ordered pairs

Answer 1

The ordered pairs are(missing values in original question are underlined)

(2, 2), (3, 7), (-4,14),(4,14), (-1,-1),(1,-1)

Explanation:

The given function is
`y=x^(2)-2`

In the first two ordered pairs we are given the value of
`x` and all we have to do is substitute for
`x` in the above function and solve for
`y`

So, for (2,...) where
`x=2,`

`y=2^(2)2-2=4-2=\boldsymbol{2}`

For the second pair, (3,...)

`y=3^(2)-2=9-2=\boldsymbol{7}`

For the last two pairs, we are given what the y value is and we substitute for y in the function equation and solve for x

For (..., 14) we get

14=x^{2}-2==>16=x^{2},so x=\pm4. This means the two possible values for x are -4 and 4

For the last pair, y=-1 which gives us

`-1=x^(2)-2== > (-1)-(-2)=x^(2)`

which gives the two possible values for x as
`x=\boldsymbol{-1}` and
`x=\bold{1}`

See the attached image for a visual depiction of these points