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soldi70 [24.7K]
3 years ago
14

You have saved $35.75. about how many tapes can you buy if each tape costs $8.47 tax included?

Mathematics
1 answer:
hammer [34]3 years ago
3 0

you can buy about 4 tapes


Hope my answer helped

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[Will mark as brainliest]
Aleks04 [339]

The answer is: f^{-1} = 4x^2-3,\quad\text{for  } x \leq 0

The inverse of a function f(x) is another function, f^{-1}(x), with the following property:

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

In other words, the inverse of a function does exactly "the opposite" of what the original function does, and so if you compute them both in sequence you return to the starting point.

Think for example to a function that doubles the input, f(x)=2x, and one that halves it: f(x)= \frac{x}{2}. Their composition is clearly the identity function f(x)=x, since you consider "twice the half of something", or "half the double of something".

In general, to invert a function y=f(x), you have to solve the expression for x, writing an expression like x = g(y). If you manage to do so, then g is the inverse of f.

In your case, you have

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

Multiply both sides by -2 to get

-2y = \sqrt{x+3}

Square both sides to get

4y^2 = x+3

Finally, subtract 3 from both sides to get

x = 4y^2 - 3

Since the name of the variables doesn't really have a meaning, you can say that the inverse function is

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

As for the domain of the inverse function, remember what we said ad the beginning: if the original function goes from set A (domain) to set B (codomain), then the inverse function goes from set B (domain) to set A (codomain). This means that the inverse function is defined on an element in B if and only if that element belongs to the range of the original function, i.e. the set of the elements of the codomain b \in B such that there exists a \in A : f(a)=b. So, we need the range of f(x).

We know that the range of g(x)=\sqrt{x} is [0,\infty). When you transform it to g(x)=\sqrt{x+3} you simply translate the graph horizontally, so the range doesn't change. But when you multiply the function times -\frac{1}{2} you affect both extrema of the range, turning it into (-\infty,0], which you can simply write as x \leq 0

4 0
3 years ago
Rewrite 2(x + 3y - 2z) using the Destributive Property
zloy xaker [14]

Answer:

2x+6y-4z

Step-by-step explanation:

multiply the two by each term and coefficient inside of the parentheses

6 0
3 years ago
What is 6x^-2 simplified
yulyashka [42]
Pemdas
parnthasees
exponnets
mult or div
add or sub

6x^-2 means
6 times x^-2

rmemeber
x^-m=1/(x^m)
6 times x^-2=6 times 1/(x^2)=6/(x^2)=\frac{6}{x^{2}}

6 0
3 years ago
Read 2 more answers
Given the quadratic equation below, determine which situation it could represent? x2 -4x = 60
yarga [219]

Answer:

The solution is x = 10 and x = -6. This quadratic could be represented in factored form as (x - 10)(x + 6) or on a graph with x-intercepts at (10,0) and (-6,0).

Step-by-step explanation:

To solve the quadratic, write the quadratic in standard form and factor the equation.

x² - 4x = 60

x² - 4x - 60 = 0

(x - 10)(x + 6) = 0

x = 10 and x = -6

4 0
3 years ago
Joseph needs to find the quotient of 3,216 divided by 8 in what play is the first digit in the quotient
Anika [276]

Answer:

3216/8 is = to 402

Step-by-step explanation:

So I am not sure what you are asking sorry

5 0
3 years ago
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