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4 years ago

10 POINTS AND WILL GIVE BRAINLIEST Given: j(x) = -2 (3/2)^x. Find j(0).

Mathematics

1 answer:

FrozenT [24]4 years ago

8 0

Answer:

Step-by-step explanation:

j(x) = -2 (3/2)^x

j(0) = -2(3/2)^0

-2(0)

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What is the inverse of this function?

kolbaska11 [484]

Answer:

$f^{-1}(x)=4x^2-3$

Step-by-step explanation:

<u>The Inverse of a Function</u>

Given a function f(x), the inverse of f, called $f^{-1}(x)$ is a function that satisfies:

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

The domain of f becomes the range of its inverse and vice-versa.

The procedure to find the inverse of the function is:

* Write the function as a two-variable equation:

* Solve the equation for x.

* Swap the variables

We are given the function:

$\displaystyle f(x)=-\frac{1}{2}\sqrt{x+3}$

Defined in the interval x ≥ -3

Note f is always negative, thus its range is f(x) ≤ 0

Now we find the inverse. Call y=f(x):

$\displaystyle y=-\frac{1}{2}\sqrt{x+3}$

Multiplying by 2:

$\displaystyle 2y=-\sqrt{x+3}$

Squaring both sides:

$\displaystyle 4y^2=x+3$

Subtracting 3:

$\displaystyle 4y^2-3=x$

Swapping variables:

$y=4x^2-3$

Thus:

$\mathbf{f^{-1}(x)=4x^2-3}$

The domain of the inverse is the range of f, thus x is restricted to

x ≤ 0

5 0

3 years ago

The tennis team is selling tickets to wash for six dollars. And they don't do not sell very much tickets, the team decreases the

schepotkina [342]

Answer:

The new cost of tickets after decrease of price at 23 % rate is $ 4.62

Step-by-step explanation:

Given as :

The initial cost of the selling tickets = $ 6

Let The final cost of selling tickets = $ x

The rate of decrease of ticket price = 23 %

Now,

The final cost of tickets = initial cost of tickets × ( 1 - $\dfrac{\textrm rate}{100}$ )

or, $ x = $ 6 × ( 1 - $\dfrac{\textrm 23}{100}$ )

or, x = $ 6 × $\frac{77}{100}$

∴ x = $ 4.62

So decrease price = x = $ 4.62

Hence The new cost of tickets after decrease of price at 23 % rate is $ 4.62 Answer

3 0

4 years ago

During a road trip Tony , Tony drove one third the distance that Lana drove. Mark drives 15 more than Lana drove .The total dist

ale4655 [162]

Answer:

The distance drive by Lana = 201 miles

The distance drive by Mark = 216 miles

The distance drive by Tony = 67 miles

Step-by-step explanation:

Given as :

The total distance cover by Lana , Tony , Mark = 484 miles

Let The distance drove by Lana = L miles

The distance drove by Tony = T

The distance cover by Mark = M

So , L + T + M = 484 miles

Now, The distance of Tony = $\frac{1}{3}$ of Lana distance

Or, T = $\frac{1}{3}$ × L

And The distance of Mark = 15 + The distance of Lana

Or, M = 15 + L

Now.

L + $\frac{1}{3}$ × L + 15 + L = 484

Or, 2 L + $\frac{L}{3}$ = 484 - 15

Or, 2 L + $\frac{L}{3}$ = 469

Or, $\frac{7 L}{3}$ = 469

Or, 7 L = 469 × 3

∴ L = $\frac{1407}{7}$

I.e L = 201

The distance drive by Lana = 201 miles

The distance drive by Mark = 15 + L =15 + 201 = 216 miles

The distance drive by Tony = $\frac{1}{3}$ × 201 = 67 miles

Hence The distance drive by each person is

The distance drive by Lana = 201 miles

The distance drive by Mark = 216 miles

The distance drive by Tony = 67 miles Answer

8 0

3 years ago

What's the answer to that question

nikdorinn [45]

Can you please put the question?

3 0

4 years ago

Read 2 more answers

For the function y = -x2 – 2, how can you find the value of y when x = 3?

Fynjy0 [20]

Answer:

y=-3x2-2

y=-8

I think it.

8 0

3 years ago

Read 2 more answers