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dybincka [34]
3 years ago
14

The function f is defined by f(x) = 2x²-1. Find f (2x).

Mathematics
1 answer:
umka21 [38]3 years ago
5 0

Answer: f(2x)=8x^2-1

Step-by-step explanation:

All that is required here is to substitute x = 2x into the right side in the same way that is done for a numeric value.

f(2x) = 2(2x)^2-1\\f(2x) = 2(4)x^2-1\\f(2x) = 8x^2-1\\

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Graph the following three equations on your own device and answer the questions below.
Alina [70]

Due to length restrictions, we kindly invite to read the explanation of this question for further details on functions.

<h3>What are the characteristics of each of the three functions?</h3>

a) In this part we must evaluate each of the three functions at the given value of x:

Case 1

f(10) = 5 · 10 + 7

f(10) = 57

Case 2

f(10) = 10² + 6

f(10) = 106

Case 3

f(10) = 2¹⁰ + 3

f(10) = 1027

b) In this part we must evaluate each of the three functions at the given value of x:

Case 1

f(100) = 5 · 100 + 7

f(100) = 507

Case 2

f(100) = 100² + 6

f(100) = 10006

Case 3

f(100) = 2¹⁰⁰ + 3

f(100) = 1.267 × 10³⁰ + 3

c) In this part we must evaluate each of the three functions at the given value of x:

Case 1

f(1000) = 5 · 1000 + 7

f(1000) = 5007

Case 2

f(1000) = 1000² + 6

f(1000) = 1000006

Case 3

f(1000) = 2¹⁰⁰⁰ + 3

f(1000) = (1.268 × 10³⁰)¹⁰ + 3

f(1000) = 10.744 × 10³⁰⁰ + 3

f(1000) = 1.074 × 10³⁰¹ + 3

e) The <em>third</em> function increases the fastest.

f) In this part we need to compare the <em>third</em> function with respect to the <em>first</em> and <em>second</em> functions:

5 · x + 7 = 2ˣ + 3

2ˣ - 5 · x   = 4

The solutions of the equation are x = - 0.675 and x = 4.81. The function will exceed the other <em>first</em> function at x = 4.81.

x² + 6 = 2ˣ + 3

2ˣ - x² = 3

The solution of the equation is x = 4.588. The function will exceed the other <em>second</em> function at x = 4.588.

g) Yes, <em>exponential</em> functions with bases greater than 1 will surpass <em>polynomic</em> function at any point x such that x > 0.

h) The domain represents the set of x-values of a function and the range represents the set of y-values of a function. Then, the domain and range of each function is:

Case 1

Domain - All <em>real</em> numbers.

Range - All <em>real</em> numbers

Case 2

Domain - All <em>real</em> numbers.

Range - [6, +∞)

Case 3

Domain - All <em>real</em> numbers.

Range - (3, +∞)

To learn more on functions: brainly.com/question/12431044

#SPJ1

5 0
1 year ago
What is the simplest value of 4⁰
Bess [88]

Answer:

1

Step-by-step explanation:

8 0
2 years ago
Giving brainlest and 20 points
Natali5045456 [20]

Answer:

C. 40 square inches but i could be wrong

4 0
2 years ago
8% of what number is 2?
azamat

Answer:

The number is 25

Step-by-step explanation:

Is means equals and of means multiply

8% *N = 2

Change to decimal form

.08 N =2

Divide by .08

.08N/.08 = 2/.08

N =25

5 0
3 years ago
Read 2 more answers
What's the elapsed time between 2:16am and 8:10pm
svet-max [94.6K]
2:16+5:54= 8:10 I think this is the answer
5 hours and 54 minutes
6 0
3 years ago
Read 2 more answers
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