Answer:
[tex] {f}^{ - 1} ( x) = - \frac{x - 3}{2} [/tex]
Step-by-step explanation:
[tex]f(x) = - 2x + 3[/tex]
To find the inverse of f(x) , equate f(x) to y
That's
y = f(x)
[tex]y = - 2x + 3[/tex]
Next interchange the terms that's x becomes y and y becomes x
That's
[tex]x = - 2y + 3[/tex]
Solve for y
Move 3 to the other side of the equation
That's
[tex] - 2y = x - 3[/tex]
Divide both sides by - 2
[tex] \frac{ - 2y}{ - 2} = \frac{x - 3}{ - 2} [/tex]
We have the final answer as
[tex] {f}^{ - 1} ( x) = - \frac{x - 3}{2} [/tex]
Hope this helps you
