Determine whether f(x)=x3 and g(x)=1/3^x are inverses

March 17, 2026Mathematics

ScanSolve AI Answer

March 17, 2026

Answer

yes, they are inverses

Step 1: Compute $f(g(x))$ .

f(g(x)) = f\left( x^{1/3} \right) = \left( x^{1/3} \right)^3

\left( x^{1/3} \right)^3 = x^{3 \cdot (1/3)} = x^1 = x

Step 2: Compute $g(f(x))$ .

g(f(x)) = g\left( x^3 \right) = \left( x^3 \right)^{1/3}

\left( x^3 \right)^{1/3} = x^{3 \cdot (1/3)} = x^1 = x

Step 3: Conclusion.

Since $f(g(x)) = x$ and $g(f(x)) = x$ , the functions $f(x)$ and $g(x)$ are inverses.

yes, they are inverses

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