We made 64 robots. We'll keep 8 of the robots and pack the rest into boxes of 4. How many boxes do we need

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.

charle [14.2K]

ANSWER

See below

EXPLANATION

Given

$f(x) = \frac{ {x}- 9 }{x + 5}$

and

$g(x) = \frac{ - 5x - 9}{x - 1}$

$(f \circ \: g)(x)= \frac{ (\frac{ - 5x - 9}{x - 1})- 9 }{(\frac{ - 5x - 9}{x - 1} )+ 5}$

$(f \circ \: g)(x)= \frac{ \frac{ - 5x - 9 - 9(x - 1)}{x - 1}}{\frac{ - 5x - 9 + 5(x - 1)}{x - 1} }$

Expand:

$(f \circ \: g)(x)= \frac{ \frac{ - 5x - 9 - 9x + 9}{x - 1}}{\frac{ - 5x - 9 + 5x - 5}{x - 1} }$

$(f \circ \: g)(x)= \frac{ \frac{ - 5x - 9x + 9 - 9}{x - 1}}{\frac{ - 5x + 5x - 5 - 9}{x - 1} }$

$(f \circ \: g)(x)= \frac{ \frac{ - 14x }{x - 1}}{\frac{ -14}{x - 1} }$

Since the denominators are the same, they will cancel out,

$(f \circ \: g)(x)= \frac{ - 14x}{ - 14} = x$

8 0

2 years ago

Michael bought 0.44 pound of slice turkey. What's the value of the digit in the hundredths place

Olegator [25]

The hundredths place is the number two to the right of the decimal(so the one in 0.01). The value would be 4.

3 0

2 years ago

Suppose that in a senior college class of 500 students itis found that 210 smoke, 258 drink alcoholic beverages, 216 eatbetween

Katarina [22]

Answer:

a)Smoke but doesn't drink alcoholic beverages

P=0.176 or 17.6%

b)eats between meals and drinks alcoholic beverages but doesn't smoke

P=0.062 or 6.2%

c.) neither smokes nor eats between meals

P=0.342 or 34.2%

Step-by-step explanation:

Using a Venn diagram with three circles, one for each bad health habit. Let us $a$ for the students that only smoke, $b$ for only drink alcoholic beverages, and $c$ for only eat between meals. Following this logic, $d$ represents smoke and drink alcoholic beverages but not eat between meals, $e$ drink alcoholic beverages and eat between meals but not smoke, $f$ eat between meals and smoke but not drink alcoholic beverages. Finally $g$ for having all the three, this means $g=52$ .

To find $f$ , subtract 52 (the three problems) from 97 because this last number represents all the students that smoke and eat between meals, including the students that have the three bad habits. The same goes for 'd' and 'e'.

$f=97-52=45$

$e=83-52=31$

$d=122-52=70$

To find $a$ , subtract $e$ , $f$ , and $g$ from the total of smokers. This is because $e$ , $f$ , and $g$ represent smoke and at least another bad habit and $a$ represents only smoking.

$a=210-d-f-g=210-70-45-52=43$