Question

If f(x) - 27x³ and g(x) = \((x)^{\frac{1}{3}}\), then gof(x) is :

• A. x
• B. 2x
• C. 3x
• D. 0

Answer 1

The Correct Option is C

To solve for \(g(f(x))\), first examine the given functions: \(f(x) = 27x^3\) and \(g(x) = x^{\frac{1}{3}}\).

The composition \(g(f(x))\) requires us to substitute \(f(x)\) into \(g(x)\):

First, compute \(f(x)\):

\(f(x) = 27x^3\)

Next, substitute \(f(x)\) into \(g(x)\):

\(g(f(x)) = g(27x^3) = (27x^3)^{\frac{1}{3}}\)

Simplify the composite function:

\((27x^3)^{\frac{1}{3}} = 27^{\frac{1}{3}} \times (x^3)^{\frac{1}{3}}\)

Calculate each component:

\(27^{\frac{1}{3}} = 3\) since 27 is a perfect cube (\(3^3\))

\((x^3)^{\frac{1}{3}} = x\)

This gives:

\(3 \times x = 3x\)

Thus, the expression for \(g(f(x))\) simplifies to \(\mathbf{3x}\).