The inverse for the function f (x) = 2 / 3 x - 3 will be f ⁻¹ (x) = 3 / 2 x + 9 / 2.
We are given the function:
f (x) = 2 / 3 x - 3
we need to find the inverse of the function.
First we will write the function in the form of x.
y = 2 / 3 x - 3
y + 3 = 2 / 3 x
2 x = 3 y + 9
x = 3 / 2 y + 9 / 2
So, the inverse function will be:
f ⁻¹ (x) = 3 / 2 x + 9 / 2.
Therefore, the inverse for the function f (x) = 2 / 3 x - 3 will be f ⁻¹ (x) = 3 / 2 x + 9 / 2.
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