If f(x) = 3^x and g(x) = 2x + 5, at which value of x is f(x) < g(x)? A. -1
B. 2
C. -3
D. -4

A) x = -1

Step-by-step explanation:

 for x = 4

Step-by-step explanation:

If

and  

Then for which value of "x" does ?

So start by evaluating what  is:

Then,we have to find for which value of x

so we write g(x) explicitly:

Work Shown:

First find f(2)

f(x) = 3x-1

f(2) = 3(2)-1 ... replace every x with 2

f(2) = 6-1

f(2) = 5

The equation g(x) = f(2) is the same as g(x) = 5 since f(2) = 5

g(x) = 2x-3

5 = 2x-3 replace g(x) with 5

2x-3 = 5

2x = 5+3 ... add 3 to both sides

2x = 8

x = 8/2 divide both sides by 2

x = 4

 for x = 4

Step-by-step explanation:

If

and  

Then for which value of "x" does ?

So start by evaluating what  is:

Then,we have to find for which value of x

so we write g(x) explicitly:

Step-by-step explanation:

Given are three functions, f, g and h.  We are to check the validity of the statements from 1 to 5

1) Avg rate of change of functions in the interval [2,3]

False

2) False, From the graph given we find that it is false

3) True since f(4) is higher than other function value at 4.

4) h(8) = 128+40+2 =170.   f(8) = 6563

Hence false.

5) f'(x) =3^x lnx:  g'(x) = 20:  h'(x) = 4x+5

False because when x=1, rate of change of f = 0<g'(x)

Last statement  a quantity increasing exponentially eventually exceeds a quantity growing quadratically or linearly

is true

Step-by-step explanation:

Given are three functions, f, g and h.  We are to check the validity of the statements from 1 to 5

1) Avg rate of change of functions in the interval [2,3]

False

2) False, From the graph given we find that it is false

3) True since f(4) is higher than other function value at 4.

4) h(8) = 128+40+2 =170.   f(8) = 6563

Hence false.

5) f'(x) =3^x lnx:  g'(x) = 20:  h'(x) = 4x+5

False because when x=1, rate of change of f = 0<g'(x)

Last statement  a quantity increasing exponentially eventually exceeds a quantity growing quadratically or linearly

is true

3.5 and 10/3

Step-by-step explanation:

just took the quiz

3.5 and 10/3

Step-by-step explanation:

just took the quiz

Your answer is B

B) x+5

Step-by-step explanation:

x = 5

f(x) = 4x + 8 = 4(5) + 8 = 28

g(x) = 2x − 3 = 25 − 3 = 29

A quantity increasing exponentially eventually exceeds a quantity increasing linearly.