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Nitella [24]
3 years ago
8

To determine whether the inverse of a function is a function you can perform the horizontal line test.

Mathematics
1 answer:
iris [78.8K]3 years ago
7 0

Answer:

\boxed{\text{TRUE}}

Step-by-step explanation:

If a horizontal line intersects the graph of a function in all places at exactly one point (the horizontal line test), the inverse of the function is also a function.

For example, the inverse of a hyperbola (like ƒ(x) =1/x) is a function, because every horizontal line intersects with the graph at exactly one point.

However, the inverse of a parabola (like ƒ(x) = x²) is not a function, because a horizontal line intersects with the graph at two points.

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The radius of a sphere is 13 cm. What is the surface area of the sphere? Round to the nearest tenth
AlekseyPX

Answer:

2123.72 cm²

Step-by-step explanation:

Hope it helps

3 0
3 years ago
What is meaning of irrational exponents.
sweet [91]

Answer:

Here

Step-by-step explanation:

Irrational exponents are non repeating or infinite decimals while rational exponents are rational numbers. The value of an irrational exponent when calculated is approximate in nature while the value of rational exponent is exact.

4 0
2 years ago
4) Suppose y varies inversely with the SQUARE ROOT of x.
Savatey [412]

Answer:

Variation equation: y = k/√x

constant of variation: 200

Variation Equation by plugging the value of k: y = 200/√x

Step-by-step explanation:

If y varies inversely with the SQUARE ROOT of x, then;

y = k/√x

If  x = 4, y = 100.

100 = k/√4

100 = k/2

200 = k

k = 200

Substitute into the expression

y = k/√x

y = 200/√x

7 0
3 years ago
Remember to show work and explain. Use the math font.
vichka [17]

Answer:

\large\boxed{1.\ f^{-1}(x)=\sqrt[12]{3^x}}\\\\\boxed{2.\ f^{-1}(x)=\sqrt[4]{3^x}}\\\\\ \boxed{3.\ f^{-1}(x)=\sqrt[3]{4^{7-x}}}

Step-by-step explanation:

(a^n)^m=a^{nm}\\\\\log_ab=c\iff a^c=b\\\\a^{\log_ax}=x\\\\n\log_ab=\log_ab^n\\\\\log_ab+\log_ac=\log_a(bc)\\============================\\\\1.\\y=3\log_3x^4\to y=\log_3(x^4)^3\to y=\log_3x^{12}

2.\\y=\log_3x^4\\\\\text{Exchange x and y. Solve for y:}\\\\\log_3y^4=x\Rightarrow3^{\log_3y^4}=3^x\Rightarrow y^{4}=3^x\\\\y=\sqrt[4]{3^x}\\-------------------------

3.\\y=-\log_4x^3+7\\\\\text{Exchange x and y. Solve for y:}\\\\-\log_4y^3+7=x\qquad\text{subtract 7 from both sides}\\\\-\log_4 y^3=x-7\qquad\text{change the signs}\\\\\log_4y^3=7-x\Rightarrow4^{\log_4y^3}=4^{7-x}\\\\y^3=4^{7-x}\Rightarrow y=\sqrt[3]{4^{7-x}}

7 0
3 years ago
Amazon was valued at 430 billion dollars. Write this number in scientific notation
pshichka [43]

Answer:

430 billion (430,000,000,000) is 4.3 x 10^11 in scientific notation

3 0
3 years ago
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