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uranmaximum [27]
3 years ago
14

What is the solution to the system of equations graphed below? y=x+3 y=3x+1

Mathematics
1 answer:
Mademuasel [1]3 years ago
8 0

Answer:

(1, 4)

Step-by-step explanation:

y=x+3

y=3x+1

y=x+3

x+3=3x+1

x=3x-2

-2x=-2

x=1

y=1+3

y=4

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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
BRAINLIEST.In which quadrant does the point (-5, 21) lie?
DanielleElmas [232]

Answer:

Point (-5,21) would end up in quadrant II (2).

Step-by-step explanation:

It would end up in quadrant 2 because x=-5 which means it would go left.

y=21 which means it would go up.

Because of this, the point would end up in the top left of the graph which is quadrant 2.

4 0
2 years ago
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