A function f (x) is given below. Find the graph of the member of the family that satisfies .
A)
B)
C)
D)
E)

Question

A function f (x) is given below. Find the graph of the member of the family  that satisfies  . ​  ​
A)​ ​ 
B)​ ​ 
C)​ ​ 
D)​ ​ 
E)​​ ​

Quizplus · Accepted Answer

The given function is:
f(x) = (x-1)/(x+2)

To find the member of the given family that satisfies f(2x + 1) = 3, we substitute x = (y-1)/2 in f(x) and solve for y such that f(2x + 1) = 3.

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

Now, substituting y = 2x+1, we have

f(y) = (y-3)/(y+1)

f(y) = 3 gives us:

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

y-3 = 3(y+1)

y-3 = 3y+3

2y = -6

y = -3

Therefore, the member of the given family that satisfies f(2x+1) = 3 is:

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

which is option C.

A Function F (X) Is Given Below