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Sloan [31]
2 years ago
12

F(x) = 1/2x2 +2x - 6 ?

Mathematics
1 answer:
Fed [463]2 years ago
8 0
F(x)= 2x-5 i believe
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For which function is f(x) equal to f^1(x) ( answer choices in picture )
Sonja [21]

Answer:

C. f(x)=\frac{x+1}{x-1}

Step-by-step explanation:

Let's find the inverse of each of the given options.

Option A:

f(x)=\frac{x+6}{x-6}\\y=\frac{x+6}{x-6}

To find f^{-1}(x), replace 'x' with 'y' and 'y' with 'x'. This gives,

x=\frac{y+6}{y-6}

Rewrite in terms of 'y'. This gives,

x(y-6)=y+6\\xy-6x=y+6\\xy-y=6x+6\\y=\frac{6x+6}{x-1}

The given function y=\frac{6x+6}{x-1}\ne y=\frac{x+6}{x-6}

So, option A is incorrect.

Option B:

f(x)=\frac{x+2}{x-2}\\y=\frac{x+2}{x-2}

To find f^{-1}(x), replace 'x' with 'y' and 'y' with 'x'. This gives,

x=\frac{y+2}{y-2}

Rewrite in terms of 'y'. This gives,

x(y-2)=y+2\\xy-2x=y+2\\xy-y=2x+2\\y=\frac{2x+2}{x-1}

The given function y=\frac{2x+2}{x-1}\ne y=\frac{x+2}{x-2}

So, option B is incorrect.

Option C:

f(x)=\frac{x+1}{x-1}\\y=\frac{x+1}{x-1}

To find f^{-1}(x), replace 'x' with 'y' and 'y' with 'x'. This gives,

x=\frac{y+1}{y-1}

Rewrite in terms of 'y'. This gives,

x(y-1)=y+1\\xy-x=y+1\\xy-y=x+1\\y=\frac{x+1}{x-1}

The given function y=\frac{x+1}{x-1}\ equals\ y=\frac{x+1}{x-1}

So, option C is correct.

Option D:

f(x)=\frac{x+5}{x-5}\\y=\frac{x+5}{x-5}

To find f^{-1}(x), replace 'x' with 'y' and 'y' with 'x'. This gives,

x=\frac{y+5}{y-5}

Rewrite in terms of 'y'. This gives,

x(y-5)=y+5\\xy-5x=y+5\\xy-y=5x+5\\y=\frac{5x+5}{x-1}

The given function y=\frac{5x+5}{x-1}\ne y=\frac{x+6}{x-6}

So, option D is incorrect.

Therefore, only option C is correct.

7 0
3 years ago
Five workers are hired to seed a field by hand. Each is given a plot which is 6x12 feet in size. What is the total area of the f
Lorico [155]

Answer:

360 feet

Step-by-step explanation:

multiple 6 by 12 to get the area of the individual plot of land given to a single worker.

Then multiply by 5 for all 5 workers getting the same plot of land.

3 0
3 years ago
Find the product of 670 and 4
Usimov [2.4K]
The product of 670 and 4 is 2,680
7 0
3 years ago
Read 2 more answers
Help please!<br><br> Help would be appreciated.
kotegsom [21]

Answer:

\displaystyle 157,5

Step-by-step explanation:

\displaystyle 3\frac{3}{4}\:quibs = 1\:slep \\ \\ 3\frac{3}{4} \times 42 = 157\frac{1}{2} = 157,5

I am joyous to assist you anytime.

5 0
3 years ago
Help!! i also need the work please!!
alex41 [277]

Answer:

1. $1.40

2.$1.75

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
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