Question

Math help plz

Answer 1

Find the domain and range of the following function. \[F(x) = (1+3)^{3/2}\]

Answer 2

Are you allowed to use a computer or calculator for this?

Answer 3

Neither

Answer 4

Yeah just use a graphing calculator

Answer 5

Show work

Answer 6

Well how are we supposed to know neither

Answer 7

I’m only allowed to show what i know

Answer 8

@TheConMan did you mean \(F(x) = (x + 3)^{3/2}\)

Answer 9

It specifically said in the course that if i get caught with a graphing cal, they’ll disown me

Answer 10

No hero. Wait, let me draw

Answer 11

rough course

Answer 12

\(a^{c/b} = \sqrt{a^c}\)

Answer 13

Wait, where are we starting from? Domain? Ok

Answer 14

Wait, let me draw.

Answer 15

Well, yes, we still need to recognize what we're dealing with before we attempt to find the domain.

Answer 16

Is that right?

Answer 17

Not exactly.

Answer 18

I don't know where you get the extra 3 from

Answer 19

That’s part of the power

Answer 20

You wrote two threes though.

Answer 21

Let me write the rule again. I don't think it was clear for you

Answer 22

No I didn’t. Show me.

Answer 23

Oh it looked like a three. It's actually a two.

Answer 24

.....

Answer 25

There's no need to put the tail on the root like that. It really did look like a three

Answer 26

Anyways the point is you now have a square root to deal with when finding the domain

Answer 27

How do i do that?

Answer 28

Do you not remember what to do in this case? Set the expression under the root \( \ge 0\)

Answer 29

Are you going to finish solving for \(x\)?

Answer 30

So the domain is al real numbers except x has to be equal or bigger than -1

Answer 31

Am I right?

Answer 32

What da?:ö

Answer 33

You can describe it in words as \(x\) is all real numbers greater than or equal to -1

Answer 34

The domain is simply written as \([-1, \infty)\) or \(-1 \le x \le \infty\) or just \(x \ge -1\)

Answer 35

You can write using set notation as well

Answer 36

But interval notation and inequality notation are standard.

Answer 37

Is my domain right tho?

Answer 38

Why are you trying to write it in set notation. There's many different forms of it. And it's better to just use inequality or interval notation

Answer 39

I jus wanna get it over with...

Answer 40

It depends on what your teacher prefers. I don't recognize the way you've written it. I've never seen set notation written that way. Like I said, different schools use different forms of set notation which is why I don't like it. Too many varying forms.

Answer 41

But inequality notation and interval notation are universally recognized

Answer 42

Ok let’s find the range now ::)

Answer 43

Just find the inverse of the function

Answer 44

Not inverse again...uhg ;/

Answer 45

Hold on, let e draw, u check

Answer 46

You're supposed to square both sides.

Answer 47

That's how you eliminate the 2

Answer 48

What did i do?

Answer 49

Square both sides not take a root to eliminate the 2

Answer 50

The 2 is already a root

Answer 51

You perform the inverse of the root to eliminate it which is squaring

Answer 52

Nope, the 1/2 is still a root

Answer 53

you should have \(x^2\) on the LHS

Answer 54

I’m falling asleep 😴

Answer 55

I need a power nap

Answer 56

Apply the cube root to both sides

Answer 57

I’ll be back in a hour....dnt go. K

Answer 58

then subtract the 1

Answer 59

What is the domain of the function?

Answer 60

of the inverse* that is

Answer 61

I can plug-in negative numbers in a cube root func right

Answer 62

Keep in mind we have a square root for the original function so the range will be limited by that.

Answer 63

I’m plug-in in numbers in the inverse func to find the dom of the original func

Answer 64

I mean to find range

Answer 65

Yes, you are but the domain of the inverse is more limited than what it appears to be

Answer 66

Hang on, let me see something

Answer 67

I say all real numbers

Answer 68

Well, the restriction on the range of the original function also restricts the domain of the inverse.

Answer 69

Yes

Answer 70

In order to find the lowest value of the range you have to evaluate the lower bound of the domain of the original function which is x = -1. Evaluate f(-1).

Answer 71

That's the lower bound of the range

Answer 72

Ok what’s left

Answer 73

the upper bound

Answer 74

How

Answer 75

When you find the domain and range of functions you're trying to find the lower and upper bounds of both

Answer 76

Which is why it is best to think beyond the "all real numbers" mentality

Answer 77

I can’t keep my eye open...

Answer 78

Brb after a power nap

Answer 79

Take a nap. Come back later.

Answer 80

K let’s go.

Answer 81

We were looking for the upper bound. We found the lower bound.

Answer 82

@hero how do we find the upper bound of the graph?

Answer 83

So you found the inverse of the function and found that the domain would be all real numbers if the domain of the original function was not bound by the square root. And you found that the lower bound of the range of the original function is zero. This implies that the domain of the inverse is \([0, \infty)\)

Answer 84

So it follows that the range of the original function is ...

Answer 85

Give me a second to think

Answer 86

Trying to recall the rule, the domain of the inverse is the range of the original function... is also that [0,infinite)

Answer 87

If the domain of the inverse func is [0,infinite), it implies that the range of the original func is also the same

Answer 88

For complex problems like these, is it better to plot some damn points and find the range and domain of the function or do i have to algebraically prove everytime?

Answer 89

@Hero

Answer 90

Plotting points is always useful to get a better understanding of the behavior of the function.

Answer 91

It's a great go-to move if you are confused about the shape or behavior of the function. So feel free to do so.

Answer 92

What about tests and exams.. how should i approach the problem and btw is my range correct

Answer 93

Yes, the range is correct. For the exam, you want to make sure you know the general graphs of each parent function and their domain and range. You want to for example know the difference between the behavior of a cubic function and the behavior of a quadratic function.

Answer 94

I see k thanks vro. On to the next question.