Question

The function below does not have an inverse. Restrict the domain of the function so that the restricted function has an inverse.
f(x) = 3(x + 5)2 - 1
Restricted domain.
x ≥

Answer 1

What am I supposed to do here?

Answer 2

That is a "squared," yes?

Answer 3

o yes. it is. my bad.

Answer 4

f(x)=3(x+5)^2-1

Answer 5

You need to find the vertex of that parabola and only use one side of it or the other... When you invert it, you end up with more than one y value for some of the x values.

Answer 6

x>=-5

Answer 7

so use, x= -b/(2a) to find the x-value of the vertex then you can use the graph above that point.

Answer 8

o and the last part should be x ≥ ___ (blank)

Answer 9

oh - oops... it's already in the right format LOL yes, x=-5

Answer 10

could you explain/show work please

Answer 11

so half of the parabola is to the right of that x-value and the other half is to the left. Choose the part you are asked for and when you invert it, there will be no problem with it being a function

Answer 12

f(x)=3(x+5)^2-1 the vertex is (-5,-1) because it is in the format y=n(x-h)^2+k where (h,k) is the vertex

Answer 13

i calculated the inverse . its has
sqrt(y+1/3) which should be greateer than 0 for gods sake no negative numbers under root. so if y>-1 corresponding expression also greater than -1. so solve for x

Answer 14

the number is positive 5... how did get a negative 5?

Answer 15

@mrslaybms

Answer 16

@mariomintchev do you understand why the function given, i.e.:
\[f(x)=3(x+5)^2-1\]does NOT have an inverse?

Answer 17

because its squared?

Answer 18

but do you what that "means"?

Answer 19

umm

Answer 20

have you talked about the 'vertical line test' in class at all?

Answer 21

o yeah

Answer 22

cant touch more than one point when a vertical line is drawn

Answer 23

in response to the 5 vs -5 question, Mario... the formula is (x-h) so what number is subtracted from the x in (x-5)? It's just 5, not -5.

Answer 24

1. the function will return some value for every value of x you put into it.
2. however, there are pairs of values for x which will give you the same value for the function (this is because the function contains a squared term as you suggested)
3. this means that if you know the value of the function, there is no way of knowing which of the pair of x values it came from
this is what makes it not have an inverse

Answer 25

so the answer was -5 because its the inverse?

Answer 26

in response to the vertical line test, exactly! :) SO,,,, if the original graph, before you find it's inverse has more then one point on a HORIZONTAL line, it's inverse will have more than one point on a VERTICAL line. Does that make sense?

Answer 27

o cause it can be 2 positives that give u the same answer and 2 negatives that can give u the same answer...

Answer 28

2 * 2 = 4 and -2 * -2 = 4

Answer 29

@mrslaybms i guess

Answer 30

Here are a couple other examples to help you with the 5 part... If y =(x+3)^2-1, it's vertex would be (-3,-1). You use the opposite of the number in the ( ) and the exact number on the outside. So... if y=(x-6)^2+3, it's vertex would be (6,3) and y=(x-2)^2-4 would be (2,-4).

Answer 31

2 points 2 answers... which means its not a one-on-one function... im guessing...

Answer 32

i see i see