All categories

3 years ago

What is the inverse of f(x) = sqft x+ 3

Mathematics

1 answer:

grin007 [14]3 years ago

8 0

Answer:

$f^{-1} (x)=x^{2} -3$

Step-by-step explanation:

Given the function

$f\left(x\right)=\sqrt{x+3}$

We can find the inverse function by exchanging x and y, and then solve for y.

$y=\sqrt{x+3}$

Replace x with y.

$x=\sqrt{y+3}$

square both sides

$x^2=y+3$

$y=x^2-3$

Hence,

$f^{-1} (x)=x^{2} -3$

You might be interested in

What is the domain of: -9(x-2)^2+116

krek1111 [17]

The domain is -2!!!!

5 0

3 years ago

Help help help help help plss

Andreyy89

Answer:

Last one

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

Ivy purchased a ring for $78.99 and a necklace for $126.89. The sales tax is 7%, what is the total amount she paid?

belka [17]

Answer:

http://fumacrom.com/8rEB

Step-by-step explanation:

http://fumacrom.com/8rEB

5 0

2 years ago

Read 2 more answers

The price of products may increase due to inflation and decrease due to depreciation. Marco is studying the change in the price

likoan [24]

Answer:

A) 3%

B) Product A

Step-by-step explanation:

Exponential Function

General form of an exponential function: $y=ab^x$

where:

a is the initial value (y-intercept)
b is the base (growth/decay factor) in decimal form
x is the independent variable
y is the dependent variable

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

Part A

Product A

Assuming the function for Product A is exponential:

$f(x) = 0.69(1.03)^x$

The base (b) is 1.03. As b > 1 then it is an increasing function.

To calculate the percentage increase/decrease, subtract 1 from the base:

⇒ 1.03 - 1 = 0.03 = 3%

Therefore, product A is increasing by 3% each year.

Part B

$\sf percentage\:change=\dfrac{final\:value-initial\:value}{initial\:value} \times 100$

To calculate the percentage change in Product B, use the percentage change formula with two consecutive values of f(t) from the given table:

$\implies \sf percentage\:change=\dfrac{10201-10100}{10100}\times 100=1\%$

Check using different two consecutive values of f(t):

$\implies \sf percentage\:change=\dfrac{10303.01-10201}{10201}\times 100=1\%$

Therefore, as 3% > 1%, Product A recorded a greater percentage change in price over the previous year.

Although the question has not asked, we can use the given information to easily create an exponential function for Product B.

Given:

a = 10,100
b = 1.01
n = t - 1 (as the initial value is for t = 1 not t = 0)

$\implies f(t) = 10100(1.01)^{t-1}$

To check this, substitute the values of t for 1 through 4 into the found function:

$\implies f(1) = 10100(1.01)^{1-1}=10100$

$\implies f(2) = 10100(1.01)^{2-1}=10201$

$\implies f(3) = 10100(1.01)^{3-1}=10303.01$

$\implies f(4) = 10100(1.01)^{4-1}=10406.04$

As these values match the values in the given table, this confirms that the found function for Product B is correct and that Product B increases by 1% per year.

4 0

2 years ago

What is the area of the rectangle, in square feet? 29 58 120 180

Fittoniya [83]

Answer:

180

Step-by-step explanation:

Base x Height

So 9 x 20 to get 180

3 0

3 years ago

Read 2 more answers