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3 years ago

What is the inverse of the function f(x) = 2x + 1?

Mathematics

2 answers:

adoni [48]3 years ago

8 0

$f(x)=2x+1\\\\y=2x+1\\2x=y-1\\x=\dfrac{y-1}{2}\\\\f^{-1}(x)=\dfrac{x-1}{2}$

hodyreva [135]3 years ago

4 0

Answer:

The inverse f-1(x) = ( x - 2) / 2.

Step-by-step explanation:

Let 2x + 1 = y

Now find x in terms of y:

2x = y - 1

x = (y - 1) / 2

Replace the x by the inverse f-1(x) and the y by x, so we have:

f-1(x) = ( x - 2) / 2.

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2 years ago

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Triangle DEF (not shown) is similar to ABC shown, with angle B congruent to angle E and angle C congruent to angle F. The length

Bezzdna [24]

Answer:

Area of ΔDEF is $45\ cm^2$ .

Step-by-step explanation:

Given;

ΔABC and ΔDEF is similar and ∠B ≅ ∠E.

Length of AB = $2\ cm$ and

Length of DE = $6\ cm$

Area of ΔABC = $5\ cm^2$

Solution,

Since, ΔABC and ΔDEF is similar and ∠B ≅ ∠E.

Therefore,

$\frac{Area\ of\ triangle\ 1}{Area\ of\ triangle\ 2} =\frac{AB^2}{DE^2}$

Where triangle 1 and triangle 2 is ΔABC and ΔDEF respectively.

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$\frac{5}{Area\ of\ triangle\ 2} =\frac{2^2}{6^2}\\ \frac{5}{Area\ of\ triangle\ 2}=\frac{4}{36}\\ Area\ of\ triangle\ 2=\frac{5\times36}{4} =5\times9=45\ cm^2$

Thus the area of ΔDEF is $45\ cm^2$ .

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2 years ago

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What is the slope of the trend line drawn into the scatter plot?

mario62 [17]

Formula for slope: $\frac{y2-y1}{x2-x1}$
Plug in points given: $\frac{136-27}{13-2} 
= \frac{109}{11} = 9.9 = 9 \frac{9}{10} (Rounded) 
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Slope: $9.9 = 9 \frac{9}{10}$

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3 years ago

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Diego's sister is twice his age minus 9 years. She is also as old as half the sum of the ages of Diego and both of his 12-year-o

slava [35]

Answer:

Diego is 14 years old.

Sister is 19

Step-by-step explanation:

x = Diego's age

x + 24

2x-9 = 2

First to get rid of the fraction we multiply each side by 2

2(2x-9) = 2((x+24)/2)

4x-18 = x+24

The we isolate x

4x-18 = x+24

-x+18 -x+18

3x = 42 Now we divide each side 3

3 3

x = 14

So Diego is 14

Now we can solve for his sister. We can use one of the two equations from earlier to do this.

Plug 14 in for x and then solve for his sister

2(14)-9

28-9

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3 years ago

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AVprozaik [17]

Answer:

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2 years ago

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