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3 years ago

How do you find out if the inverse of a piece wise function is a function?

Mathematics

1 answer:

cricket20 [7]3 years ago

8 0

Answer:

If it is not one-to-one, it does not have an inverse.

Step-by-step explanation:

If the output has more than 1 input, it cannot possibly be a function, meaning there is no inverse for that function.

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What postulate or theorem proves the two triangles are similar?

Keith_Richards [23]

Answer:sas

Step-by-step explanation:

6 0

3 years ago

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The area of a circle is 153.86 square meters. What is the diameter of the circle?

Yuliya22 [10]

Area of circle = πr²

Given that area = 153.86 m², find the radius:

153.86 = πr²

r² = 153.86 ÷ π

r² = 48.98

r = √48.98

r = 7 m

Diameter = Radius x 2 = 7 x 2 = 14 m

Answer: Diameter = 14 m

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3 years ago

Bob and Carl each renter the same kind of moving truck from ez move. There was a flat rental fee plus charge per mile that the t

dimulka [17.4K]

It's a linear function: y = mx + b

We have (138; 112.96); (209; 142.78)

substitute the values of x and y to the formula of slope m:

$m=\dfrac{y_2-y_1}{x_2-x_1}\\\\m=\dfrac{142.78-112.96}{209-138}=0.42$

Now we have: $y=0.42x+b$

We must find b. Substitute the value of x and y from first pair of numbers:

$112.96=0.42\cdot138+b\\\\112.96=57.96+b\ \ \ |-57.96\\\\b=55$

Answer: y = 0.42x + 55

3 0

3 years ago

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Simplify. Your answer should contain only positive exponents with no fractional exponents in the denominator.

mart [117]

Answer:

$\dfrac{x^{\frac{2}{3}}y^{\frac{1}{4}}}{4y^{2}}$ .

Step-by-step explanation:

The given expression is

$\dfrac{3y^{\frac{1}{4}}}{4x^{-\frac{2}{3}}y^{\frac{3}{2}}\cdot 3y^{\frac{1}{2}}}$

We need to simplify the expression such that answer should contain only positive exponents with no fractional exponents in the denominator.

Using properties of exponents, we get

$\dfrac{3}{4\cdot 3}\cdot \dfrac{y^{\frac{1}{4}}}{x^{-\frac{2}{3}}y^{\frac{3}{2}+\frac{1}{2}}}$ $[\because a^ma^n=a^{m+n}]$

$\dfrac{1}{4}\cdot \dfrac{y^{\frac{1}{4}}}{x^{-\frac{2}{3}}y^{2}}$

$\dfrac{1}{4}\cdot \dfrac{x^{\frac{2}{3}}y^{\frac{1}{4}}}{y^{2}}$ $[\because a^{-n}=\dfrac{1}{a^n}]$

$\dfrac{x^{\frac{2}{3}}y^{\frac{1}{4}}}{4y^{2}}$

We can not simplify further because on further simplification we get negative exponents in numerator or fractional exponents in the denominator.

Therefore, the required expression is $\dfrac{x^{\frac{2}{3}}y^{\frac{1}{4}}}{4y^{2}}$ .

5 0

4 years ago

Simplify the rational expression 6x(x+3)(x-2)/3(x-2)(x+9) A) 2x/x-3 B)2x/(x-9) C) 2x(x+3)/(x+9)

Irina-Kira [14]

Answer:

$\large\boxed{C)\ \dfrac{2x(x+3)}{(x+9)}}$

Step-by-step explanation:

$\dfrac{6x(x+3)(x-2)}{3(x-2)(x+9)}=\dfrac{6\!\!\!\!\diagup^2}{3\!\!\!\!\diagup_1}\cdot\dfrac{(x-2)}{(x-2)}\cdot\dfrac{x(x+3)}{(x+9)}=\dfrac{2x(x+3)}{(x+9)}$

6 0

3 years ago

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