Answer:
For y = 5; –3; 0; 2 ⇒ x = -31/3 ; -17/5 ; 1/2 ; ∅
Step-by-step explanation:
Given:
[tex]y=\frac{2x-1}{x+6}[/tex]
It is required to find the values of x which make y = 5; –3; 0; 2
A) y = 5
[tex]5=\frac{2x-1}{x+6}[/tex]
∴ 5 (x+6) = 2x- 1
5x + 30 = 2x - 1
5x - 2x = -1 - 30
3x = -31 ⇒ x = -31/3
B) y = -3
[tex]-3=\frac{2x-1}{x+6}[/tex]
-3(x+6) = 2x-1
-3x - 18 = 2x - 1
-5x = 17 ⇒ x = -17/5
C) y = 0
[tex]0=\frac{2x-1}{x+6}[/tex]
2x - 1 = 0
2x = 1 ⇒ x = 1/2
D) y = 2
[tex]2=\frac{2x-1}{x+6}[/tex]
∴ 2 (x+6) = 2x- 1
2x + 12 = 2x - 1
∴ 12 = -1 ⇒ no solution ⇒ ∅
Which mean there is no value of x to make y = 2
Because the domain of the given function = R - {-6}
And the range will be R - {2}
So for y = 5; –3; 0; 2 ⇒ x = -31/3 ; -17/5 ; 1/2 ; ∅
