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4 years ago

What is the inverse of the given function? y=7x^2-3

Mathematics

2 answers:

Sergeu [11.5K]4 years ago

5 0

So the answer to this equations is :
y= +/- <span>√x+3/7</span>

Alja [10]4 years ago

4 0

To find the invers of y=something
1. switch x and y
2. solve for y
3. replace y with f⁻¹(x)

so
y=7x²-3
switch x and y
x=7y²-3
solve for y
add 3
x+3=7y²
$\frac{x+3}{7} =y^2$
$\sqrt{\frac{x+3}{7}} =y$
$f^{-1}(x)= \sqrt{\frac{x+3}{7}}$
rationalizing denomenator
$f^{-1}(x)= \frac{\sqrt{7(x+3)}}{7}$

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(x^2 - x^(1/2))/(1-x^(1/2))

Levart [38]

$\frac { \left( { x }^{ 2 }-{ x }^{ \frac { 1 }{ 2 } } \right) }{ \left( 1-{ x }^{ \frac { 1 }{ 2 } } \right) }$

$\\ \\ =\frac { \left( { x }^{ 2 }-\sqrt { x } \right) }{ \left( 1-\sqrt { x } \right) } \cdot 1$

$\\ \\ =\frac { \left( { x }^{ 2 }-\sqrt { x } \right) }{ \left( 1-\sqrt { x } \right) } \cdot \frac { \left( 1+\sqrt { x } \right) }{ \left( 1+\sqrt { x } \right) }$

$\\ \\ =\frac { { x }^{ 2 }+{ x }^{ 2 }\sqrt { x } -\sqrt { x } -x }{ 1+\sqrt { x } -\sqrt { x } -x }$

$\\ \\ =\frac { -\sqrt { x } \left( 1-{ x }^{ 2 } \right) -x\left( 1-x \right) }{ \left( 1-x \right) }$

$\\ \\ =\frac { -\sqrt { x } \left( 1+x \right) \left( 1-x \right) -x\left( 1-x \right) }{ \left( 1-x \right) }$

$\\ \\ =\frac { \left( 1-x \right) \left\{ -\sqrt { x } \left( 1+x \right) -x \right\} }{ \left( 1-x \right) }$

$\\ \\ =-\sqrt { x } \left( 1+x \right) -x\\ \\ =-{ x }^{ \frac { 1 }{ 2 } }\left( 1+{ x }^{ \frac { 2 }{ 2 } } \right) -x$

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3 0

3 years ago

Read 2 more answers

A toy rocket is launched from a platform 33 feet above the ground at a speed of 83 feet per second. The height of the rocket in

yanalaym [24]

Answer:

c. 138 feet

Step-by-step explanation:

h(t) = −16t^2 + 83t + 33

At3 seconds

h(3) = -16(3^2) + 83(3) + 33

h(3) = -16(9) + 249 + 33

h(3) = -144 + 249 + 33

h(3) = 138

c. 138 feet

3 0

3 years ago

Answer fast pls .....

Fudgin [204]

1. the perimeter of a square is always 4 * side, so = 4*31/8 = 31/2 or 15 and 1/2
2. area of a square is always the side multiplied by each other, so: 9/2 * 9/2 = 81/4 or 20 and 1/4

3 0

2 years ago

Altred is saving up money for a down payment on a house. He currently has $4739, but knows he can get a loan at a lower interest

Stella [2.4K]

Given the word problem, we can deduce the following information:

Principal amount = $4739

Future amount = $5336

Interest = 5.1 % =0.051

To determine the time to accumulate the $5336, we use the compound interest formula:

$A=P(1+\frac{r}{n})^{nt}$

A=Future amount=$5336

P=Present amount=$4739

r=interest rate = 0.051

n=number of compounding periods =12

t=time in years

We also note that the number of compounding periods must be 12 since the investment is compounded monthly.

We plug in what we know:

$\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ 5336=4739(1+\frac{0.051}{12})^{12t} \\ Simplify\text{ and rearrange} \\ 5336=4739(\frac{12.051}{12})^{12t} \\ 12t=\frac{\ln\frac{5336}{4739}}{\ln\frac{12.051}{12}} \\ t=\frac{\operatorname{\ln}\frac{5,336}{4,739}}{12\operatorname{\ln}\frac{12.051}{12}} \\ Calculate \\ t=2.33 \end{gathered}$

Therefore, the answer is 2.33 years.

5 0

1 year ago

Help please with math AsAp

ella [17]

Answer:

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Step-by-step explanation:

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6 0

3 years ago