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Alik [6]
3 years ago
13

What the inverse of f(x)=4x²

Mathematics
1 answer:
Inessa05 [86]3 years ago
6 0

f(x)=4x^2\to y=4x^2\\\\\text{Interchange the y and the x}\\\\x=4y^2\\\\\text{Solve for y}\\\\4y^2=x\qquad|:4\\\\y^2=\dfrac{x}{4}\to y=\sqrt{\dfrac{x}{4}}\\\\y=\dfrac{\sqrt{x}}{\sqrt4}\\\\y=\dfrac{\sqrt{x}}{2}\\\\Answer:\ \boxed{f^{-1}(x)=\dfrac{\sqrt{x}}{2}}\ for\ x\geq0

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Tell whether the given value is a solution of the inequality. (yes or no)<br><br> -2 ≤ k/3; k = -9
olga55 [171]

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Work Shown:

-2 ≤ k/3

-2 ≤ -9/3

-2 ≤ -3

The last inequality is false because -3 should be smaller than -2 (not the other way around). Use a number line to help see this.

Since the last inequality is false, the original inequality must also be false for that particular k value. Therefore, k = -9 is not a solution.

4 0
2 years ago
You go to a local mechanic to get your tires changed. The tires cost $300. There is a 6% sales tax, but you get a 10% discount.
Romashka-Z-Leto [24]

Answer:

a) T(x)=300x+18x=318x

b) D(x)=318x-(0.1)(318)+10x\\=296.2x

c) Yes.

Step-by-step explanation:

We have that:

Tires=$300\\Tax=0.006\\Discount=0.1\\

And we have $10 free of taxes.

Making x= number of tires to buy, then we have that the total cost of tires is:

Total_{Tires}=300x

So, what we pay for taxes is given by:

Taxes=(300x)(0.06)=18x

a) Then, according to the above, we can write down the total cost before the discount as:

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b) And the total cost after discounts, is then given by:

D(x)=318x-(0.1)(318)+10x\\=296.2x

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