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3 years ago

Need help on this math problem!!!

Mathematics

1 answer:

Colt1911 [192]3 years ago

4 0

Answer:

$(fof^{-1})(x)=x$

Step-by-step explanation:

Composition of two functions f(x) and g(x) is represented by,

(fog)(x) = f[g(x)]

If a function is,

f(x) = (-6x - 8)² [where x ≤ $-\frac{8}{6}$ ]

Another function is the inverse of f(x),

$f^{-1}(x)=-\frac{\sqrt{x}+8}{6}$

Now composite function of these functions will be,

$(fof^{-1})(x)=f[f^{-1}(x)]$

= $[-6(\frac{\sqrt{x}+8}{6})-8]^{2}$

= $[-\sqrt{x}+8-8]^2$

= $(-\sqrt{x})^2$

= x

Therefore, $(fof^{-1})(x)=x$

You might be interested in

2/x + 3/y = 13 ; 5/x - 4/y = -2

Tomtit [17]

Given that

(2/x)+(3/y) = 13--------(1)

(5/x)-(4/y) = -2 -------(2)

Put 1/x = a and 1/y = b then

2a + 3b = 13 ----------(3)

On multiplying with 5 then

10a +15 b = 65 -------(4)

and

5a -4b= -2 ----------(5)

On multiplying with 2 then

10 a - 8b = -4 -------(6)

On Subtracting (6) from (4) then

10a + 15b = 65

10a - 8b = -4

(-)

_____________

0 + 23 b = 69

______________

⇛ 23b = 69

⇛ b = 69/23

⇛ b =3

On Substituting the value of b in (5)

5a -4b= -2

⇛ 5a -4(3) = -2

⇛ 5a -12 = -2

⇛ 5a = -2+12

⇛ 5a = 10

⇛ a = 10/5

⇛ a = 2

Now we have

a = 2

⇛1/x = 2

⇛ x = 1/2

and

b = 3

⇛1/y = 3

⇛ y = 1/3

<u>Answer :-</u>The solution for the given problem is (1/2,1/3)

<u>Check</u>: If x = 1/2 and y = 1/3 then

LHS = (2/x)+(3/y)

= 2/(1/2)+3/(1/3)

= (2×2)+(3×3)

= 4+9

= 13

= RHS

LHS=RHS is true

and

LHS=(5/x)-(4/y)

⇛ 5/(1/2)- 4/(1/3)

⇛(5×2)-(4×3)

⇛ 10-12

⇛ -2

⇛RHS

LHS = RHS is true

5 0

2 years ago

Multiply. Express your answer in simplest form.

kodGreya [7K]

Step-by-step explanation:

1.) First, you need to take the whole numbers (9 and 1) and set them aside.

2.) Multiply the numerators from each fraction by one another. The numerators are the numbers on the top of the fraction. (Whatever you get on that will be the numerator of the answer!)

3.) Multiply the denominators by each other as well. The denominators are the numbers on the bottom. This will be the denominator of your answer.

4.) Now, you need to multiply your whole numbers (9 and 1) together.

5.) Then, simplify or reduce your answer. (this can't be simplified, as it is already in its simplest form)

Your answer will be 9 1/66.

Your work should look like this in the end:

4 0

3 years ago

How do you find 6x=-5y

eduard

6x=-5y
-5y=6x
so the answer is y=-6/5x

5 0

3 years ago

Refer to the equation 2x − 3y = 18.

Mice21 [21]

There is the table. <3

7 0

3 years ago

Can someone please help

Vsevolod [243]

It may be convenient here to write the equation of the line as

... ∆y(x -x0) -∆x(y -y0) = 0

where (x0, y0) is a point on the line, and (∆x, ∆y) is the difference between two points on the line.

Using the first two points, we have

... (∆x, ∆y) = (-9, 10) - (-15, 5) = (6, 5)

So, the equation of the line is

... 5(x +9) -6(y -10) = 0 . . . . . . using the point (x0, y0) = (-9, 10)

... 5x -6y = -105 . . . . . . . . . . . simplify to standard form

Now, dividing by the constant on the right, we can put this into intercept form

... x/(-21) +y/(17.5) = 1

This tells us the y-intercept is (0, 17.5) and the x-intercept is (-21, 0).

_____

You can work directly with the values in the table. The y-value increases by 5 from one line to another, while the x-value increases by 6. Thus, to make the y-value decrease by 5 from the first point, we need to decrease that point's x-value by 6 to -21. That is, the x-intercept is (-21, 0).

Similarly, the x-value need to increase by only 3 from the last point. That amounts to half of the usual increase of 6. Thus the y-intercept will be the last point plus have the usual y-increase of 5, or 15+2.5 = 17.5. That is, the y-intercept is (0, 17.5).

5 0

3 years ago