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Komok [63]
3 years ago
15

Given f(x)=-1/7√16-x^2 find f^-1(x)

Mathematics
1 answer:
Vera_Pavlovna [14]3 years ago
6 0

Answer:

f^{-1}(x)=\pm \sqrt{49x^2-16}

Not a function.

Step-by-step explanation:

The given function is;

f(x)=-\frac{1}{7}\sqrt{16-x^2}

Let y=-\frac{1}{7}\sqrt{16-x^2}

Interchange x and y;

x=-\frac{1}{7}\sqrt{16-y^2}

Solve for y;

-7x=\sqrt{16-y^2}

Square both sides

(-7x)^2=(\sqrt{16-y^2})^2

49x^2^2=16-y^2

49x^2^2-16=y^2

y=\pm \sqrt{49x^2-16}

The inverse is

f^{-1}(x)=\pm \sqrt{49x^2-16}

f^{-1}(x)=\pm \sqrt{49x^2-16} is not a function because one x-value maps onto to different y-values.

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The element europium (EU) exists in nature as two isotopes: (151 EU)with a mass of 150.9196 amu & (153 EU) with a mass of 15
mixer [17]

Answer:

X = 48.014%

Y = 51.986%

Step-by-step explanation:

Given

151 EU has a mass of 150.9196 amu

153 EU has a mass of 152.9209 amu

Calculating the relative abundance of the two EU isotopes.

First condition that must be satisfied is

X + Y = 100%;

X + Y = 1. ----- Equation 1

Second Condition is;

150.9196X + 152.9209Y = 151.96 ------ Equation 2

In Equation 1; make Y the subject of formula.

So, Y = 1 - X.

Substitute (1 - X) for Y in Equation 2

150.9196X + 152.9209(1 - X) = 151.96 ----Open bracket

150.9196X + 152.9209 - 152.9209X = 151.96 ---- Collect Like Terms

150.9196X - 152.9209X = 151.96 - 152.9209

−2.0013X = -0.9609

X = -0.9609/-2.0013

X = 0.480137910358267

X = 48.014% ----- Approximated

Y = 1 - X

Y = 1 - 48.014%

Y = 0.51986

Y = 51.986% ---- Approximated

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Step-by-step explanation:

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