Functions, f and g are given by f(x)= 3+ cos x and g(x) = 2x, x is a real number. Determine the value of c for which f(g(x))= g(f(x)) where 0 x<2

Step-by-step explanation:

Given two functions, we can combine them in such a way so that the outputs of one function become the inputs of the other. This action defines a composite function. Let's take a look at what this means!

Evaluating composite functions

Example

If f(x)=3x-1f(x)=3x−1f, left parenthesis, x, right parenthesis, equals, 3, x, minus, 1 and g(x)=x^3+2g(x)=x

3

+2g, left parenthesis, x, right parenthesis, equals, x, cubed, plus, 2, then what is f(g(3))f(g(3))f, left parenthesis, g, left parenthesis, 3, right parenthesis, right parenthesis?

Solution

One way to evaluate f(g(3))f(g(3))f, left parenthesis, g, left parenthesis, 3, right parenthesis, right parenthesis is to work from the "inside out". In other words, let's evaluate g(3)g(3)g, left parenthesis, 3, right parenthesis first and then substitute that result into fff to find our answer.

Let's evaluate g({3})g(3)g, left parenthesis, 3, right parenthesis.

\begin{aligned}g(x)&=x^3+2 g(3)&=({3})^3 +2\small{\gray{\text{Plug in }x={3.}}} &={29}\end{aligned}

g(x)

g(3)

​

answer set (b) 0.5, 3/4 80% is in order from least to greatest.  

step-by-step explanation:

in order to compare rational numbers to each other, it is much easier if they are in the same form.   typically, the best form in which to evaluate rational numbers is in decimals.   in order to convert a percent to a decimal, you would divide the given percentage by 100.   you can also accomplish the conversion by moving the decimal point over two places to the left.   for example, the decimal value of 80% is 80/100, or 0.8.   in order to convert a fraction to a decimal, you need to divide the numerator by the denominator.   for example, 3/4 is 0.75.   so, for choice (b) 0.5 3/4 (0.75), 80% (0.8) is the only choice in which the numbers are in order from least to greatest.  

the answer would be d.

step-by-step explanation:

move all variables to the left side and all constants to the right side

(x−3)^2+(y−1)^2=16

this is the form of a circle. use this form to determine the center and radius of the circle.

( x − h ) 2 + ( y − k ) 2 = r 2

match the values in this circle to those of the standard form. the variable   r   represents the radius of the circle,   h   represents the x-offset from the origin, and   k   represents the y-offset from origin.

r = 4

h = 3

k = 1

the center of the circle is found at   ( h , k ) .

center:   ( 3 , 1 )

these values represent the important values for graphing and analyzing a circle.

center:   ( 3 , 1 ).

radius:   4