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What is the domain and range for the following function and its inverse? f(x)=(3x-1)/(2)?

0 votes
domain and range for the following function and its inverse
asked May 27, 2013 in ALGEBRA 1 by andrew Scholar

2 Answers

0 votes

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

3x - 1  is not equal to 0 (because of f(x) will turn zero

3x - 1 = 0    Therefore  x  = 1/3

domain = x belongs to ( -infinity , infinity) - {1/3}

for range

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

Multiply each side by 2.

2 f (x ) = [ ( 3 x -1) / 2 ] 2

2 f ( x)  = 3 x - 1

Add  1  to  each  side

2 f ( x ) + 1  =  3 x  - 1 + 1

2 f ( x )  + 1 =  3x

Then  x  =  {2 f ( x ) + 1} / 3

{2f(x ) +  1}/3  is not equal to 0.

therefore f(x) is not equal to (-1/2).

range = ( -infinity , infinity) - {-1/2}

Let  f ( x ) = y

( 3 x + 1 ) / 2  =  y

2 y  =  3 x  + 1

(  2 y  - 1 ) / 3  =  x

 Inverse  function is f'(x) = (2x - 1) / 3.

answered Jun 8, 2013 by goushi Pupil
reshown Jun 18, 2013 by moderator
Domain and range are all real numbers.
0 votes

The equation is f(x ) = (3x - 1)/2.

y = 3/2 x - 1/2

Make the table of values to find ordered pairs that satisfy the equation.

Choose values for x and find the corresponding values for y.

x

y = 3/2 x - 1/2

(x, y)

       -2 y = (3/2)(-2) - 1/2 =-7/2      (-2,-7/2)

       -1

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

(-1,-2)

0

y = (3/2)(0) - 1/2 = -1/2

(0,-1/2)

1

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

(1,1)

2

y = (3/2)(2) - 1/2 = 5/2

(2,5/2)

Draw a coordinate plane.

Plot the coordinate points.

Then sketch the graph, connecting the points with a line.

graph the equation x=y^2

Since x can be any real number, there is an infinite number of ordered pairs that can be graphed. All of them lie on the line shown.

Notice that every real number is the x - coordinate of some point on the line.

Also, every real number is the y - coordinate of some point on the line.

So, the domain and range are both all real numbers, and the relation is continuous.

answered Jul 3, 2014 by joly Scholar

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