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2 years ago

For the function f(x)=5x^3-6, find f^-1

Mathematics

1 answer:

max2010maxim [7]2 years ago

5 0

Answer:

$f^{-1}$ means the inverse function

$f^{-1}$ = $\sqrt[3]{(x + 6)/5}$

Step-by-step explanation:

$f^{-1}$ means the inverse function

to find an inverse function, flip the x and y variables and solve for y

f(x) = 5x^3 - 6

y = 5x^3 - 6

x = 5y^3 - 6

x + 6 = 5y^3

(x + 6)/5 = y^3

$\sqrt[3]{(x + 6)/5}$ = y

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3 years ago

Which of the following is the expansion of (3c + d2)6?

vovangra [49]

Answer: Option A) $729c^6 + 1,458c^5d^2 + 1,215c^4d^4 + 540c^3d^6 + 135c^2d^8 + 18cd^{10} + d^{12}$ is the correct expansion.

Explanation:

on applying binomial theorem, $(a+b)^n=\sum_{r=0}^{n} \frac{n!}{r!(n-r)!} a^{n-r} b^r$

Here a=3c, $b=d^2$ and n=6,

Thus, $(3c+d^2)^6=\sum_{r=0}^{6} \frac{6!}{r!(6-r)!} (3c)^{n-r} (d^2)^r$

⇒ $(3c+d^2)^6= \frac{6!}{(6-0)!0!} (3c)^{6-0}.(d^2)^0+\frac{6!}{(6-1)!1!} (3c)^{6-1}.(d^2)^1+\frac{6!}{(6-2)!2!} (3c)^{6-2}.(d^2)^2+\frac{6!}{(6-3)!3!} (3c)^{6-3}.(d^2)^3+\frac{6!}{(6-4)!4!} (3c)^{6-4}.(d^2)^4+\frac{6!}{(6-5)!5!} (3c)^{6-5}.(d^2)^5+\frac{6!}{(6-6)!6!} (3c)^{6-6}.(d^2)^6$

⇒ $(3c+d^2)^6= \frac{6!}{(6-)!0!} (3c)^6.d^0+\frac{6!}{(5)!1!} (3c)^5.d^2+\frac{6!}{(4)!2!} (3c)^4.d^4+\frac{6!}{(6-3)!3!} (3c)^3.d^6+\frac{6!}{(2)!4!} (3c)^2.d^8+\frac{6!}{(1)!5!} (3c).d^{10}+\frac{6!}{(0)!6!} (3c)^0.d^{12}$

⇒ $(3c+d^2)^6=(3c)^6.d^0+\frac{720}{120} (3c)^5.d^2+\frac{720}{48} (3c)^4.d^4+\frac{720}{36} (3c)^3.d^6+\frac{720}{48} (3c)^2.d^8+\frac{720}{120} (3c).d^{10}+.d^{12}$

⇒ $(3c+d^2)^6=729c^6 + 1,458c^5d^2 + 1,215c^4d^4 + 540c^3d^6 + 135c^2d^8 + 18cd^{10} + d^{12}$

3 0

3 years ago

Read 2 more answers

Solve the following system of equations by substitution and select the correct answer below:

Cerrena [4.2K]

Answer:

Step-by-step explanation:

Start with variable x.
4x - 6y = 28
Substitute the variables for numbers.
4(1) - 6(-4) = 28
Solve the new equation
4 + -24 = 28

Move to the second equation with variable y.
8x - 4y = 24
Substitute variables
8(1) - 4(-4) = 24
Solve
8 - (-16) = 24

The answer is A, x = 1, y = -4

3 0

2 years ago

13, 15, 17, x, 20, 21; The median is 18.

Mamont248 [21]

To find the median

⇒ must define what is a median

⇒Definition of median: middle number of an ordered set

Lets look at the information given

Set when ordered: 13,15, 17,x,20,21 with median of 18

⇒ In this case, there is an even number of numbers

⇒ to find the median

⇒ must find average of two numbers closest to the middle

⇒ which are 'x' and '17' which is equal to the given median 18

Let's set up the equation:

$\frac{x+17}{2} =18\\x+17=36\\x=19$

Answer: x = 19

Hope that helps!

6 0

2 years ago

9/10 - _ = 1/5 mathematics

marin [14]

Answer:

x=7/10

Step-by-step explanation:

1/5=2/10

9/10- =2/10

Substitute the blank with X

9/10- X =2/10

x=7/10

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2 years ago

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