Answer:
Step-by-step explanation:
f⁻¹(x) is the inverse of f(x).
y = 4x − 9. To find the inverse, switch x and y and solve for y.
x = 4y − 9
x + 9 = 4y
y = (x + 9) / 4
So the inverse function is:
f⁻¹(x) = (x + 9) / 4
ANSWER
[tex]{f}^{ - 1}(x) = \frac{x + 9}{4} [/tex]
EXPLANATION
The given function is
f(x)=4x-9
Let
y=4x-9
Interchange x and y.
x=4y-9
Add 9 to both sides,
x+9=4y
Divide both sides by 4
[tex] \frac{x + 9}{4} = y[/tex]
[tex]y = \frac{x + 9}{4} [/tex]
Therefore,
[tex] {f}^{ - 1}(x) = \frac{x + 9}{4} [/tex]
