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Naddik [55]
3 years ago
13

Identify the inverse function of f(x) = VX - 2 + 3.

Mathematics
2 answers:
laiz [17]3 years ago
7 0

Answer:

\huge\boxed{f^{-1}(x) = (x-3)^2+2}

Step-by-step explanation:

f(x) = \sqrt{x-2} + 3

Replace y = f(x)

y = \sqrt{x-2} + 3

Exchange x and y

x = \sqrt{y-2}+3

Solve for y

x = \sqrt{y-2}+3

Subtracting both sides by 3

x - 3 = \sqrt{y-2}

Taking square on both sides

(x-3)^2 = y -2

Adding 2 to both sides

y = (x-3)^2+2

Substitute y = f^{-1}(x)

f^{-1}(x) = (x-3)^2+2

skelet666 [1.2K]3 years ago
3 0

Answer:

<h3>\boxed{ {f}^{ - 1} (x) =  {(x - 3)}^{2}  + 2}</h3>

Option D is the correct option

Step-by-step explanation:

\mathsf{f(x) =  \sqrt{x - 2}  + 3}

Replace f(x) with y

\mathsf{y =   \sqrt{x - 2}  + 3}

Interchange variables

\mathsf{x =  \sqrt{y - 2}  + 3}

\mathsf{{(x - 3)}^{2}  =  {( \sqrt{y - 2)} }^{2} }

\mathsf{ {(x - 3)}^{2}  = y - 2}

\mathsf{ y =  {(x - 3)}^{2}  + 2}

Replace y with f ⁻¹( x )

\mathsf{ {f}^{ - 1} (x) =  {(x - 3)}^{2}  + 2}

Hope I helped!

Best regards!

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sweet [91]

Answer:

2

Step-by-step explanation:

4 can be divided by 2 & 2 can be divided by 2

5 0
3 years ago
The coordinates of point Lon a coordinate grid are (-2,-4) Point L is reflected across the y-axis to obtain point M and across t
aivan3 [116]

Answer:

Point M = (2, -4)

Point N = (2, 4)

Step-by-step explanation:

Point L = (-2,-4)

If it is reflected over y-axis, it's y-coordinate remains the same and x-coordinate will change into it's opposite.

Point M = (2, -4)

The, it is reflected over x-axis, it's x-coordinate remains the same and y-coordinate will change into it's opposite.

Point N = (2, 4)

7 0
3 years ago
What is (3.5×10^4) written in science notation with 4 significant digits
asambeis [7]
It's already written in scientific notation, but since it needs 2 more significant digits, it would be 3.500×10^4.
4 0
4 years ago
1. Which ordered pairs are solutions to the inequality –3x + y ≥ 7?
Murrr4er [49]
Q1. The answers are (–1, 8), (0, 7), (3, 18)

<span>–3x + y ≥ 7
</span>Let's go through all choices:

<span>(–2, –3) 
</span>(-3) * (-2) + (-3) ≥ 7
6 - 3 ≥ 7
3 ≥ 7       INCORRECT

(–1, 8) 
(-3) * (-1) + 8 ≥ 7
3 + 8 ≥ 7
11 ≥ 7       CORRECT

(0, 7) 
(-3) * 0 + 7 ≥ 7
0 + 7 ≥ 7
7 ≥ 7       CORRECT

(1, 9) 
(-3) * 1 + 9 ≥ 7
-3 + 9 ≥ 7
6 ≥ 7       INCORRECT

(3, 18) 
(-3) * 3 + 18 ≥ 7
-9 + 18 ≥ 7
9 ≥ 7       CORRECT



Q2. The answers are:
5x + 12y ≤ 80
x ≥ 4
<span>y ≥ 0
</span>
<span>x - small boxes
</span><span>y - large boxes

</span>He has x small boxes that weigh 5 lb each and y large boxes that weigh 12 lb each <span>on a shelf that holds up to 80 lb:
5x + 12y </span>≤ 80

Jude needs at least 4 small boxes on the shelf: x ≥ 4

Let's check if y can be 0:
5x + 12y ≤ 80
5x + 12 * 0 ≤ 80
5x + 0 ≤ 80
5x ≤ 80
x ≤ 80 / 5
x ≤ 16

x ≥ 4 can include x ≤ 16

So, y can be 0: y ≥ 0
8 0
3 years ago
Solve for all valúes of x
malfutka [58]

Answer:

2x/(x+3) +3/(x-3) = 8/(x^2

[2x(x-3) +3(x+3)]\( x^2 - 9) =8/(x^2 -9)

2x^2 -6x +3x +9=8 (x^2 -9) /(x^2 -9)

2 x^2 -3x +9 -8=0

2 x^2 -3x +1 =0

2x^2 -2x -1x +1 =0

2x(x-1) -1(x-1)=0

(x-1)(2x-1)=0

either, or, 2x-1=0

x-1 =0 2x =1

x =1 x= 1/2

hence, x= 1, 1/2

7 0
3 years ago
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