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3 years ago

If the function f(x) = mx + b has an inverse function, which statement must be true?

2 answers:

7 0

F(x) = mx + b is just equal to the equation
y = mx + b

In order for us to get the inverse function, then we can interchange x to y and y to x
y = mx + b
x = my + b

Then we need to find y
x = my + b
-my = -x + b
my = x - b
y = (x-b) / m
f(x) = (x - b) / m

Mariulka [41]3 years ago

5 0

Answer:

m ≠ 0

Step-by-step explanation:

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For what value of constant c is the function k(x) continuous at x = 0 if k =

nlexa [21]

The value of constant c for which the function k(x) is continuous is zero.

<h3>What is the limit of a function?</h3>

The limit of a function at a point k in its field is the value that the function approaches as its parameter approaches k.

To determine the value of constant c for which the function of k(x) is continuous, we take the limit of the parameter as follows:

$\mathbf{ \lim_{x \to 0^-} k(x) = \lim_{x \to 0^+} k(x) = 0 }$

$\mathbf{\implies \lim_{x \to 0 } \ \ \dfrac{sec \ x - 1}{x}= c }$

Provided that:

$\mathbf{\implies \lim_{x \to 0 } \ \ \dfrac{sec \ x - 1}{x}= \dfrac{0}{0} \ (form) }$

Using l'Hospital's rule:

$\mathbf{\implies \lim_{x \to 0} \ \ \dfrac{\dfrac{d}{dx}(sec \ x - 1)}{\dfrac{d}{dx}(x)}= \lim_{x \to 0} sec \ x \ tan \ x = 0}$

Therefore:

$\mathbf{\implies \lim_{x \to 0 } \ \ \dfrac{sec \ x - 1}{x}=0 }$

Hence; c = 0

Learn more about the limit of a function x here:

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2 years ago

I don't understand this problem.. please help.. 33 • 32 + 12 ÷ 4

Vlad [161]

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4 years ago

Read 2 more answers

Given: 2x + 11 = 15 Prove: x = 2 Statements Reason 1. 2x + 11 = 15 1. Given 2. 2x = 4 2. 3. X = 2 3. Division Property of Equali

wariber [46]

Answer:

Statements Reasons

1. 2x + 11 = 15 1. Given

2. 2x = 4 2. Subtraction Property of Equality

3. X = 2 3. Division Property of Equality

Step-by-step explanation:

An equation can be solved and its solution proven using algebraic theorems and properties. To create a proof, form two columns. Label one side Statements and the other Reasons.

Begin your proof listing the any information given to you. List as the reason - Given.

Then list the next step which here would be to subtract by 11 on both side. The reason is Subtraction Property of Equality. Subtraction is the inverse of addition. Inverse axiom is another acceptable reason.

Then divide both sides by 2. The reason is Division Property of Equality or Inverse axiom once again. See the proof below.

Statements Reasons

1. 2x + 11 = 15 1. Given

2. 2x = 4 2. Subtraction Property of Equality

3. X = 2 3. Division Property of Equality

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3 years ago

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4 years ago

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