Answer:
see explanation
Step-by-step explanation:
let y = f(x) and rearrange making x the subject, that is
y = [tex]\frac{2x-3}{x+1}[/tex] ← multiply both sides by (x + 1)
y(x + 1) = 2x - 3 ← distribute left side
xy + y = 2x - 3 ( subtract y from both sides )
xy = 2x - 3 - y ( subtract 2x from both sides )
xy - 2x = - 3 - y ← factor out x from each term on the left side
x(y - 2) = - 3 - y ← divide both sides by y - 2
x = [tex]\frac{-3-y}{y-2}[/tex] factor out - 1 on numerator and denominator
x = [tex]\frac{-(3+y)}{-(2-y)}[/tex]
Change y back into terms of x, thus
[tex]f^{-1}[/tex](x) = [tex]\frac{3+x}{2-x}[/tex] = [tex]\frac{x+3}{2-x}[/tex]
Answer:
f-1(x) = (x + 3)/ (2 - x) or -(x + 3 / (x - 2).
Step-by-step explanation:
Let y = (2x - 3)/(x + 1)
We find x in terms of y:
Cross multiply:
y(x + 1) = 2x - 3
xy + y = 2x - 3
y + 3 = 2x - xy
x(2 - y) = y + 3
x = (y + 3) / (2 - y)
Now replace x by f-1(x) and y by x, we get:
f-1(x) = (x + 3)/ (2 - x).
Your answer was correct. You found the same result written in a different form.
If we multiply the above by -1 / -1 we get
-(x + 3) / -(2 - x)
= -(x + 3) / (x - 2).
