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(A) Given functions are $f(x)=2x-3$ and $g(x)=x^3+5$. First,we find the composite function $(f \circ g)(x) = f(g(x))$. $(f \circ g)(x) = 2(g(x)) - 3 =

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$-2$

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(A) Given functions are $f(x)=2x-3$ and $g(x)=x^3+5$. First,we find the composite function $(f \circ g)(x) = f(g(x))$. $(f \circ g)(x) = 2(g(x)) - 3 = 2(x^3+5) - 3 = 2x^3 + 10 - 3 = 2x^3 + 7$. Let $y = (f \circ g)(x) = 2x^3 + 7$. To find the inverse $(f \circ g)^{-1}(y)$,we solve for $x$ in terms of $y$: $y - 7 = 2x^3$ $x^3 = \frac{y-7}{2}$ $x = \left(\frac{y-7}{2}\right)^{1/3}$. Thus,$(f \circ g)^{-1}(y) = \left(\frac{y-7}{2}\right)^{1/3}$. Now,substitute $y = -9$: $(f \circ g)^{-1}(-9) = \left(\frac{-9-7}{2}\right)^{1/3} = \left(\frac{-16}{2}\right)^{1/3} = (-8)^{1/3} = -2$.

$f: R \rightarrow R$ and $g: R \rightarrow R$ are two functions such that $f(x)=2x-3$ and $g(x)=x^3+5$. Then,$(f \circ g)^{-1}(-9)$ is

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