3. Simplify. *<br> 5m3 + 2m– 7m3

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

2 years ago

The area of the rectangular floor in Tamara's room is 95 5/6 square

White raven [17]

Area of rectangle is width × length
which means area of rectangular floor in Tamara's room = width of room × length of room
-> 95 ⅚ sq feet = 8 ⅓ feet × length of
->(95 + 5/6) sq feet = (8 + 1/3) feet × length of room
->575/6 sq feet = 25/3 feet × length of room
length of room = (575/6)/(25/3)
= 575 × 3/6 × 25)
= 23/2
= 11 ½ feet

8 0

2 years ago

Read 2 more answers

The area of a patio is 72 square feet. The length of the patio is 1 foot longer than the width. What is the width of the patio?

mote1985 [20]

I know there must be an equation to do this, but there is a simpler way.
Just factor number 72 into two numbers which, when multiplied, equal 72. Two of such numbers are 9 and 8, and you can see that the difference between those two numbers is just 1. So that is the answer to your question - the length of the patio is 9 feet, whereas the width is 8 feet.

4 0

2 years ago

8 4/5 - 5 1/10 <br> Please Help

Romashka-Z-Leto [24]

Answer:

my g get a fraction calculator

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

The object of the game is to toss a beanbag in the circular hole of a 48-by-24-inch board. If the diameter of the circle is 6 in

larisa [96]

Answer:

Geometric probability of an object hitting a circular hole is 0.0245.

Step-by-step explanation:

We have given,

A board of size 48 by 24 inch. There is a circular hole in the board having diameter 6 inches.

So,

Area of a board = 48 × 24 = 1152 square inches

And area of circular hole = π×r² {where r = diameter/2 = 6 / 2 = 3 inches}

Area of circular hole = π×3² = 9π = 28.27 square inches

Now, we need to find the geometric probability of an object will hit the circle.

Geometric probability = Area of circular hole / Area of board

Geometric probability = $\frac{28.27}{1152}$

Geometric probability = 0.0245

hence geometric probability of an object hitting a circular hole is 0.0245.

6 0

2 years ago

3. Simplify. * 5m3 + 2m– 7m3 – 8m