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3 years ago

Algebraically find the inverse of a function

Mathematics

1 answer:

Savatey [412]3 years ago

6 0

9514 1404 393

Answer:

1) f⁻¹(x) = 6 ± 2√(x -1)

3) y = (x +4)² -2

5) y = (x -4)³ -4

Step-by-step explanation:

In general, swap x and y, then solve for y. Quadratics, as in the first problem, do not have an inverse function: the inverse relation is double-valued, unless the domain is restricted. Here, we're just going to consider these to be "solve for ..." problems, without too much concern for domain or range.

1) x = f(y)

x = (1/4)(y -6)² +1

4(x -1) = (y-6)² . . . . . . subtract 1, multiply by 4

±2√(x -1) = y -6 . . . . square root

y = 6 ± 2√(x -1) . . . . inverse relation

f⁻¹(x) = 6 ± 2√(x -1) . . . . in functional form

3) x = √(y +2) -4

x +4 = √(y +2) . . . . add 4

(x +4)² = y +2 . . . . square both sides

y = (x +4)² -2 . . . . . subtract 2

5) x = ∛(y +4) +4

x -4 = ∛(y +4) . . . . . subtract 4

(x -4)³ = y +4 . . . . . cube both sides

y = (x -4)³ -4 . . . . . . subtract 4

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The area of a rectangular painting is 5/8 square yard. The width is 3/4 yard. What is the length of the painting?

vfiekz [6]

Answer:

The answer is

<h2> $\frac{5}{6} \: \: \: \: yards \\$ </h2>

Step-by-step explanation:

Area of a rectangle = length × width

Since we are finding the length of the rectangle

$length = \frac{area}{width} \\$

From the question

area = 5/8 square yards

width = 3/4 yard

So we have

$length = \frac{5}{8} \div \frac{3}{4} \\ = \frac{5}{8} \times \frac{4}{3} \\ = \frac{5}{2} \times \frac{1}{3}$

We have the final answer as

$\frac{5}{6} \: \: \: \: yards \\$

Hope this helps you

3 0

3 years ago

Which equation is y = 2x2 – 8x + 9 rewritten in vertex form?

pishuonlain [190]

we have

$y=2x^{2} -8x+9$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$y-9=2x^{2} -8x$

Factor the leading coefficient

$y-9=2(x^{2} -4x)$

Complete the square. Remember to balance the equation by adding the same constants to each side

$y-9+8=2(x^{2} -4x+4)$

$y-1=2(x^{2} -4x+4)$

Rewrite as perfect squares

$y-1=2(x-2)^{2}$

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therefore

the answer is the option C

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3 years ago

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7nadin3 [17]

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Step-by-step explanation:

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3 years ago

Which equation is a direct variation function? y = x y = 1/4 x + 2 y = x2 , y = 4,

Soloha48 [4]

Answer:

$y=x$ and $y=\frac{1}{4}x$

Step-by-step explanation:

We know,

'Direct Variation function' is the function where two quantities vary directly i.e. variables x and y are said to be directly varying if 'y=kx' where k is the constant of variation.

Thus, from the options, we see that the function,

$y=x$ is varying directly with the constant of variation i.e. k = 1.

$y=\frac{1}{4}x$ is also varying directly with constant $k=\frac{1}{4}$