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guajiro [1.7K]
3 years ago
9

Determine whether the statements are True or False. Justify your answer with an explanation.

Mathematics
1 answer:
frez [133]3 years ago
7 0

Problem 1

<h3>Answer: False</h3>

---------------------------------

Explanation:

The notation (f o g)(x) means f( g(x) ). Here g(x) is the inner function.

So,

f(x) = x+1

f( g(x) ) = g(x) + 1 .... replace every x with g(x)

f( g(x) ) = 6x+1 ... plug in g(x) = 6x

(f o g)(x) = 6x+1

Now let's flip things around

g(x) = 6x

g( f(x) ) = 6*( f(x) ) .... replace every x with f(x)

g( f(x) ) = 6(x+1) .... plug in f(x) = x+1

g( f(x) ) = 6x+6

(g o f)(x) = 6x+6

This shows that (f o g)(x) = (g o f)(x)  is a false equation for the given f(x) and g(x) functions.

===============================================

Problem 2

<h3>Answer: True</h3>

---------------------------------

Explanation:

Let's say that g(x) produced a number that wasn't in the domain of f(x). This would mean that f( g(x) ) would be undefined.

For example, let

f(x) = 1/(x+2)

g(x) = -2

The g(x) function will always produce the output -2 regardless of what the input x is. Feeding that -2 output into f(x) leads to 1/(x+2) = 1/(-2+2) = 1/0 which is undefined.

So it's important that the outputs of g(x) line up with the domain of f(x). Outputs of g(x) must be valid inputs of f(x).

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judith's family went on a cross-country trip. they drove exactly 232 miles a day for 12 days. how many miles did they drive?​
Maksim231197 [3]

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2 years ago
The perimeter of a rectangle downtown courtyard is 174 feet. The width of the rectangle is twice the length. Find the length and
kirill [66]

Answer:

Step-by-step explanation:

L = Length

W = Width

W = 2L

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2 years ago
Give a counterexample for the statement all square roots are irrational numbers
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Step-by-step explanation:

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3 years ago
A car lot owner is trying to get rid of this year's inventory to make room for the new vehicles. He paid $25,599 for a red truck
Paha777 [63]

Answer:

<h2>14%</h2>

Step-by-step explanation:

Step one

given data

Cost price of vehicle=  $25,599

Selling price of vehicle= $22,000

Required

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Step two:

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The mark down percentage use is 14%

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