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Solve the following.
If f : mathbbR → mathbbR, f(x) = x³ and g : mathbbR → mathbbR, g(x) = 2x² + 1, and mathbbR is the…
If $f : \mathbb{R} \to \mathbb{R}$, $f(x) = x^3$ and $g : \mathbb{R} \to \mathbb{R}$, $g(x) = 2x^2 + 1$, and $\mathbb{R}$ is the set of real numbers, then find $fog(x)$ and $gof(x)$.
Answer
Answer
$fog(x) = f(g(x)) = (2x^2+1)^3$
$gof(x) = g(f(x)) = 2(x^3)^2 + 1 = 2x^6 + 1$
Hence $fog(x) = (2x^2+1)^3$ and $gof(x) = 2x^6+1$.
Final answer: $fog(x) = (2x^2+1)^3,\; gof(x) = 2x^6+1$