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Taya2010 [7]
3 years ago
15

What is f–1(8)?? Please select the best answer

Mathematics
2 answers:
notka56 [123]3 years ago
5 0

Answer:

f^{-1}(8)=\frac{3}{2}

Step-by-step explanation:

Given f(x)=2x+5

We have to find f^{-1}(8)

In order to find f^{-1}(x) we have to make x as the subject of the formula

Let us assume f(x)=y

⇒2x+5=y

Subtracting both sides by 5

2x+5-5=y-5

2x=y-5

Dividing both sides by 2

\frac{2x}{2}=\frac{y-5}{2}

⇒x=\frac{y-5}{2}

Now substituting y with x

we have f^{-1}(x)=\frac{x-5}{2}

Now f^{-1}(8)=\frac{8-5}{2}

=\frac{3}{2}

So option (ii) is correct


Lynna [10]3 years ago
3 0

Answer:

Choice B is correct answer.

Step-by-step explanation:

From question statement , we observe that

A function is given and we have to find inverse of this function. Then, we have to find the f⁻¹(8).

f(x) = 2x+5

put f(x) = y in above equation, we get

y = 2x+5

adding -5 to both sides of above equation,we get

y-5 = 2x+5-5

y-5 = 2x

dividing by 2 to both sides of equation,we get

y-5 / 2 = 2x/ 2

y-5 / 2 = x

swapping equation,we get

x = y-5 / 2

put f⁻¹(y) = x in above equation,we get

f⁻¹(y) = y-5 / 2

replace y with x in above equation

f⁻¹(x) = x-5 / 2

we have to find  f⁻¹(8) .

putting x = 8 in above equation,we get

f⁻¹(8) = 8-5/2

f⁻¹(8) = 3/2 which is the answer.

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Consider the attached ellipse. Let the sun be at the right focus. Then perihelion is at right vertex on the x-axis and aphelion is at the left vertex on the x-axis.

The distances:

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Then

\left\{\begin{array}{l}a-c=741,000,000\\a+c=817,000,000\end{array}\right.

Add these two equations:

2a=1,558,000,000 \\ \\a=779,000,000

and subtract first equation from the second:

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The equation for the planet's orbit is

\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1\Rightarrow \dfrac{x^2}{606,841,000,000,000,000}+\dfrac{y^2}{605,397,000,000,000,000}=1.

7 0
3 years ago
Solve for x………………………
k0ka [10]

4×11+1=45

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A motorboat travels 244 kilometers in 4 hours going upstream and 749 kilometers in 7 hours going downstream. What is the rate of
Kryger [21]

Answer:

Speed of Motorboat = 84 kmph

Speed of Current = 23 kmph

Step-by-step explanation:

Distance Equation is:

D = RT

Where

D is distance

R is rate

T is time

Downstream rate is rate of boat PLUS current

Upstream rate is rate of boat MINUS current

Let rate of boat be "x" and rate of current be "c".

From first statement, we can write:

244 = (x - c)(4)

From second statement, we can write:

749 = (x + c)(7)

The first equation becomes:

244 = 4x - 4c

The second equation becomes:

749 = 7x + 7c

Multiplying first equation by 7 , we have:

7 * [244 = 4x - 4c] = 1708 = 28x - 28c

Multiplying 2nd equation by 4, we have:

4 * [749 = 7x + 7c] = 2996 = 28x + 28c

Now we add up these equations (in bold):

1708 = 28x - 28c

2996 = 28x + 28c

----------------------------

4704 = 56x

x = 4704/56

x = 84

Now using this value and plugging in original equation, we can find "c":

244 = 4x - 4c

244 = 4(84) - 4c

244 = 336 - 4c

4c = 92

c = 92/4

c = 23

<u>Speed of Motorboat = 84 kmph</u>

<u>Speed of Current = 23 kmph</u>

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-13, 3.48, 12, 103 .................
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Solve the following multiplication problem.<br><br> 11 cu. yd. 17 cu. in. × 135
Gekata [30.6K]

Answer:

69,286,455 cu inches

Step-by-step explanation:

<u>Step 1: Convert yards to inches</u>

1 cu yard = 46656 cu inches

11 cu yard = y cu inches

<em>Cross multiply</em>

y = 11 x 46656

y = 513216 cu inches

<u>Step 2: Find total inches</u>

513216 + 17 = 513233 cu inches

<u>Step 3: Multiply total inches by 135</u>

513233 x 135 = 69,286,455 cu inches

!!

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