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3 years ago

Algebraically determine the inverse of the function f(x)= 12x2+5.

Mathematics

1 answer:

aivan3 [116]3 years ago

7 0

Answer:

Step-by-step explanation:

f(x)= 12x2+5 should be written as f(x) = 12x^2 + 5; the " ^ " symbol signifies exponentiation and is mandatory.

Here's how we find the inverse function.

1. Apply the horizontal line test. if a horizontal line intersects the graph in more than one place, the function is not one-to-one and does not have an inverse for all x. However, if we focus on only [0, infinity), this part of the graph does have an inverse, which we can find as follows:

2. Replace 'f(x)' with 'y: y = 12x^2 + 5

3. Interchange x and y: x = 12y^2 + 5

x - 5

4. Solve for y: 12y^2 = x - 5; y^2 = ------------

x - 5

y = √(----------)

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Elect the correct answer. What are the solutions of this quadratic equation?

zvonat [6]

Answer:

Rewrite equation as:

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a = 1 b = 2 c = 2

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Step-by-step explanation:

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3 years ago

A rancher is ordering a box of cube-shaped salt licks. the edge length of each salt lick are 5/12 foot. is the volume of one sal

strojnjashka [21]

Answer:

0.0723 cubic feet < 1 cubic foot.

Step-by-step explanation:

A cube-shaped salt lick is ordered by a rancher and the length of each salt lick is $\frac{5}{12}$ foot.

Therefore, the side length of each salt lick of cube-shape is $\frac{5}{12}$ foot.

So, the volume of each salt lick is $(\frac{5}{12} \times \frac{5}{12} \times \frac{5}{12}) = \frac{125}{1728} = 0.0723$ cubic feet.

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4 years ago

A store is selling 5 types of hard candies: cherry, strawberry, orange, lemon and pineapple. How many ways are there to choose:(

Volgvan

Answer:

The number of ways of selecting of n items form r different items = $^{(n+r-1)}C_{(r-1)}$

A store is selling 5 types of hard candies: cherry, strawberry, orange, lemon and pineapple.

A) How many ways are there to choose 32 candies?

So, n = no. of items = 32

r = no. of types of items = 5

So, No. of ways to choose 32 candies = $^{(32+5-1)}C_{(5-1)}$

= $^{36}C_{4}$

= $\frac{36!}{4!(36-4)!}$

= $58905$

So, No. of ways to choose 32 candies is 58905

B)32 candies with at least a piece of each flavor?

Out of 32 you choose 5 candies of different types

So, Remaining candies = 32 - 5 = 27

So, No. of ways to choose 27 candies = $^{(27+5-1)}C_{(5-1)}$

= $^{31}C_{4}$

= $\frac{31!}{4!(31-4)!}$

= $31465$

So, No. of ways to choose 32 candies with at least a piece of each flavor is 31465

C) 32 candies with at least 4 cherry and at least 6 lemon?

So, you already choose 6+4= 10

So, remaining candies = 32-10 = 22

So, No. of ways to choose 22 candies = $^{(22+5-1)}C_{(5-1)}$

= $^{26}C_{4}$

= $\frac{26!}{4!(26-4)!}$

= $14950$

Hence No. of ways to choose 32 candies with at least 4 cherry and at least 6 lemon is 14950

8 0

4 years ago

Thehe minimum weight of the 20 student is 20 kg.If their range is 20 kg,find the maximum weight and the coefficient of range

Anastasy [175]

Answer:

1/3

Step-by-step explanation:

Range=x maximum (xm) –x minimum (x0)

xm=20+20=40

Coefficient of Range= xm–x0/xm+x0

=40-20/40+20

=20/60

=2/6

=1/3

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3 years ago

What is the gcf of 64 and 16

Naily [24]

The gcf of 64 and 16 is16

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3 years ago