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Mathematics

1 answer:

Gelneren [198K]2 years ago

7 0

Answer:

I think it is 80 12

Step-by-step explanation:

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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

Midge baked 6 cookies and 4 brownies. Midge only has enough ingredients to bake at most 25 cookies or brownies total. Let x repr

GenaCL600 [577]

Given:
baked: 6 cookies and 4 brownies
can bake 25 more either cookies or brownies

Let x represent the number of more cookies that Midge can bake
Let y represent the number of more brownies that Midge can bake.

cookies = 6 + x
brownies = 4 + y

(6 + x) + (4 +y) ≤ 25
10 + x + y ≤ 25
x + y ≤ 25 - 10
x + y ≤ 15

y ≤ 15 - x

The following graphs best represents the relationship between x and y is:

line joining ordered pair 0, 15 and 7, 8 and the region below this line which lies in the first quadrant is shaded