Let g (x) = 3x+2 and f (x) = x-2 / 3 find the value. g (f(2))

a. 1
b. 0
c. 2
d. 1/3

Answers

Let g(x)=3x+2 and f(x)=x-2/3

f(2) = 2 -2/3

f(2) = 6/3 - 2/3

f(2) = 4/3

g(f(2)) = 3(4/3) +2

g(f(2)) = 4 + 2

g(f(2)) = 6

Answer

6

A. 0

Step-by-step explanation:

first you need to find g(0)

g(0) = 3(0) + 2 = 2

then you find f(g(0)) = f(2)

f(2) = 2 - 2 /3 = 0/3 = 0

x^2+\dfrac1{x^2}=3\implies x^4+1=3x^2\implies x^4-3x^2+1=0

By the quadratic formula,

x^2=\dfrac{3\pm\sqrt5}2\implies x^2+1=\dfrac{5\pm\sqrt5}2

Then

(x^2+1)^2=\dfrac{25\pm10\sqrt5+5}4=\dfrac{15\pm5\sqrt5}2

\implies\dfrac{x^2}{(x^2+1)^2}=\dfrac{\frac{3\pm\sqrt5}2}{\frac{15\pm5\sqrt5}2}=\dfrac{3\pm\sqrt5}{15\pm5\sqrt5}

Multiply numerator and denominator by the denominator's conjugate:

\dfrac{3\pm\sqrt5}{15\pm5\sqrt5}\cdot\dfrac{15\mp5\sqrt5}{15\mp5\sqrt5}=\dfrac{45\pm15\sqrt5\mp15\sqrt5-25}{15^2-(5\sqrt5)^2}=\dfrac{20}{100}=\dfrac15

1.) 1 1/3 or 4/3

2.) 6

3.) 8

Step-by-step explanation:

Function composition substitutes more than just values or constants. It substitutes functions inside another function. Solve each expression by starting inner most and working to outermost.

1.) f(g(0))  = 1 1/3

Let g(x)=3x+2 and f(x)= x-2/3.

Begin with g(0) = 3(0) + 2 = 2.

Substitute x = 2 into f(x).

f(2) = (2) - 2/3 = 1 1/3

2.) g(f(2))  = 6

Let g(x)=3x+2 and f(x)= x-2/3.

Begin with f(2) = 2 - 2/3 = 1 1/3.

Substitute x = 1 1/3 into g(x).

g(1 1/3) = 3( 1 1/3) + 2 = 3(4/3) + 2 = 4 + 2 = 6

3.) g(g((0))

Let g(x)=3x+2.

Begin with g(0) = 3(0) + 2 = 2.

Substitute x = 2 into g(x).

g(2) = 3(2) + 2 = 8

1. 2(-3) + 4

 -6 + 4 = -2

2. -4^2 - 3

   16 - 3 = 13

3.  2 (m + 2) + 4

   2m + 4 + 4

   2m + 8

   2m = -8

   m = -4

4. i forgot how to do this. sorry :'(

(f-g)(x) = f(x) - g(x)

= 2x - 4 - (x² + 3)

(f-g)(x) = -x² + 2x - 7

(f•g)(x) = 2g(x) - 4

= 2(x² + 3) - 4

fg(x) = 2x² + 6x - 4

1gives you  2-2/3 = 1 and 1/32 gives you 3(4/3) + 2 = 63 gives you 3(2)+2 = 8

OPTION C.

Step-by-step explanation:

In order to solve the given exercise, you can follow these steps:

1. Given the following function f(x):

f(x)=\frac{x-2}{3}

You must substitute x=2 into the function f(x). Then:

f(2)=\frac{(2)-2}{3}

2. Evaluating, you get:

f(2)=\frac{0}{3}\\\\f(2)=0

3. Now, the next step is to substitute f(2)  into the function g(x):

g (x) = 3x+2\\\\g (f(2)) = 3(0)+2

4. Finally, evaluating, you get the following result:

g (f(2)) = 0+2\\\\g (f(2)) =2

You can identify that it matches with the Option C.

OPTION C.

Step-by-step explanation:

In order to solve the given exercise, you can follow these steps:

1. Given the following function f(x):

f(x)=\frac{x-2}{3}

You must substitute x=2 into the function f(x). Then:

f(2)=\frac{(2)-2}{3}

2. Evaluating, you get:

f(2)=\frac{0}{3}\\\\f(2)=0

3. Now, the next step is to substitute f(2)  into the function g(x):

g (x) = 3x+2\\\\g (f(2)) = 3(0)+2

4. Finally, evaluating, you get the following result:

g (f(2)) = 0+2\\\\g (f(2)) =2

You can identify that it matches with the Option C.



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