If f: R -> R is defined by f(x) = 2x – 3 and g: R -> R is defined by g(x) = x³ + 5, then (fog)⁻¹(-9) is equal to:

Given functions $f(x) = 2x - 3$ and $g(x) = x^3 + 5$.

First, find the composite function $(fog)(x)$:

$(fog)(x) = f(g(x)) = f(x^3 + 5)$

Substitute $x^3+5$ into $f(x)$: $2(x^3 + 5) - 3$

$(fog)(x) = 2x^3 + 10 - 3 = 2x^3 + 7$

Now, we need to find $(fog)^{-1}(-9)$.

Let $(fog)^{-1}(-9) = k$. By definition of inverse functions, this means $(fog)(k) = -9$.

Using the expression for $(fog)(x)$ we found:

$2k^3 + 7 = -9$

Subtract 7 from both sides: $2k^3 = -9 - 7$

$2k^3 = -16$

Divide by 2: $k^3 = -8$

Take the cube root of both sides: $k = \sqrt[3]{-8}$

$k = -2$

Therefore, $(fog)^{-1}(-9) = -2$.