Question

Find gof and fog, if

f(x) = 8x^3 and g(x) = x^(1/3)

Answer 1

Answer:

Step-by-step explanation:

fog(x)=f(g(x))

=f(x^1/3)

=8(x^3*^1/3)

=8x

Answer 2

Answer:

$gof(x)=2x\\fog(x)=8x$

Step-by-step explanation:

$Given \\f(x)=8x^{3}---(1)\\g(x)=x^{\frac{1}{3}}---(2)$

$i)gof(x)\\=g[f(x)]\\=g[8x^{3}] \:\:[from \:(1)]\\=\big(8x^{3}\big)^{\frac{1}{3}}\\=\left(\big(2x\big)^{3}\right)^{\frac{1}{3}}\\=\big(2x\big)^{3\times \frac{1}{3}}\\</p><p>= 2x$

$ii)fog(x)\\=f[g(x)]\\=f[x^{\frac{1}{3}}]$

$=8[\big(x^{\frac{1}{3}}\big)^{3}]\\=8x^{3\times \frac{1}{3}}\\=8x$

Therefore,

$gof(x)=2x\\fog(x)=8x$

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