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Andrej [43]
2 years ago
11

Danika concludes that the following functions are inverses of each other because f(g(x)) = x. Do you agree with Danika? Explain

your reasoning.
f(x) = |x|
g(x) = –x
Mathematics
2 answers:
Mumz [18]2 years ago
8 0

that Danika needs to find g compose f

that g(f(x)) must also equal x

that g(f(x)) = –x

arsen [322]2 years ago
5 0
We cannot agree with Danika. Why? Well, The reasoning is given as follows:

Two functions are inverses of each other if and only if it is true that the composition function is given by:

f(g(x))=x

Everything is ok up to this point, right?. But let's prove that this is not fulfilled for these functions, then:

f(x)=\left | x \right | \\ \\ g(x)=-x \\ \\ f(g(x))=\left| -x \right |=\left | -1 \right | \left | x \right |=\left | x \right |  \\ \\ \therefore f(g(x))=\left | x \right | \neq x
<span>
As you can see we did not obtain the function that matches the definition of </span>inverse functions. For that reason <em>we can't agree with Danika</em>.
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25 + 11 hope this helps

Step-by-step explanation:

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What is the equation of the line whose y-intercept is 3 and slope is 1? y = x - 3 y = x 3 y = 3x 1 user: what is the slope of a
Lesechka [4]
A)

y = mx + c

<span>y = 1x + 3
</span>
<span>y = x + 3
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b)
y =  2x   ?   5            comparing to y = mx + c,   slope = m

slope = 2.

But for a perpendicular line, we take the negative reciprocal,

= -1/2   =   -1/2
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3 years ago
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2. Apples cost $0.99 per pound. Aaliyah has a
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Step-by-step explanation:

2.14=0.99a-0.50

2.64=0.99a

4 0
3 years ago
Consider the function f(x) defined by the finite set f(x)={(−2,5),(0,4),(1,−3)}. Graph the function f(x) and the transformation
Lelu [443]

let's calculate it step by step.

I'll assume that the function we look for is quadratic, because we only got 3 points

I plotted the 3 points for checking the equation later, and some intuited insight. see screenshot 1

let's write the general form of quadratic equations:

f(x) = a*x² + b*x + c

our goal is to correctly determine a, b and c

since we know from the 2nd point that

f(0) = a*0² + b*0 + c = 4

we can say

<em><u>c = 4</u></em>

this one comes almost for free

now to the next point, the 3rd one

f(1) = a*1² + b*1 + 4 = -3

we can write it as

a + b + 4 = -3

we can rearrange that to

<em><u>a = -b -7</u></em>

lastly, to the first point

f(-2) = a*(-2)² + b*(-2) + 4 = 5

simplified to

4a -2b + 4 = 5

since sort of defined a, let's plug it into our newest equation

4*(-b-7) -2b +4 = 5

we just swapped a for what its equal to.

now we just got numbers and b's

simplify it to

-4b -28 -2b +4 = 5

-6b -24 = 5

-6b = 29

<em><u>b = -29/6</u></em>

now we use the exact value of b to plug it into the rather simple equation from earlier. into this one

a = -b -7

a = -(-29/6) -7

a = 29/6 -42/6

<em><u>a= -13/6</u></em>

now that we got a, b and c we can write the whole equation

<em><u>f(x) = -13/6*x² -29/6*x +4</u></em>

see the graphic check in screenshot 2

second part of the problem:

if we want to move the whole graph 4 units down, we effectivly just cancel the +4 part

g(x) = f(x) -4 = f(x) = -13/6*x² -29/6*x +4 -4

<em><u>g(x) = -13/6*x² -29/6*x</u></em>

see screenshot 3 for the graph

5 0
2 years ago
NEED HELP ASAP, WILL GIVE BRAINLIEST
dangina [55]

Answer:

b.332.2

Step-by-step explanation:

3 0
3 years ago
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