Question

@ganeshie8 @BSwan @amistre64

Answer 1

u have 10 sec to post :P before i go

Answer 2

Given \[f (x) = 2x ^{2}+2\]

Answer 3

Find the domain of f(x).

Find the range of f(x).

Find the inverse of f(x).

Answer 4

Domain of f(x) are all the possible values of 'x'.
Are there any restrictions to x? No. Then what are the values of 'x' which satisfy f(x)?

Range of f(x) is the range of all the possible values of f(x). What all can be the possible values of f(x). As it turns out, there is no definitive way of knowing this. But we cn try out some tricks.

\[f(x) = 2x^2 + 2\]
\[y = 2x^2 + 2\]
\[y - 2 = 2x^2\]
\[x = \pm \sqrt{\frac{y-2}{2}}\]

We know one restriction, the RHS will have. That is, that, \[\frac{y-2}{2}\] will always be greater then or equal to zero. Why? Because if it lesser than zero (or negative) then the square root will give us an imaginary number which does not fall in its real range or domain. So basically we can get this inequality from there, that: \[\frac{y-2}{2} \ge 0\]
Which implies: \[y > 2\]\[f(x) > 2\]
So the range of f(x) essentially is: \((2, \infty)\)

Getting this till here?

Answer 5

so what was the domain

Answer 6

What do you think the domain'll be?

Answer 7

idk how to figure that out

Answer 8

Do you know what 'domain' means in functions?

Answer 9

If f(x) is a function.
On an elementary level:
All possible values of f(x) represents the 'range'.
All the allowed values of 'x' in the function f(x) represents the 'domain'.

In this question the function is: \[f(x) = 2x^2 + 2\]What can be the possible values of 'x' here? Everything right? Because, there -are- no restrictions on 'x'. I can input all values of 'x'.

Understood this? :)

Answer 10

yes understood so what do i put down as the domain and range on the work sheet

Answer 11

@ganeshie8

Answer 12

Another way to approach is draw the graph