Question

Find gof and fog, if \(x^{\frac{1}{3}}\)

(i) f(x) = |x|, and g(x) = |5x – 2|.

(ii) f(x) = 8x³ and g(x) = \(x^{\frac{1}{3}}\)

Answer 1

(i) f(x) = |x|, and g(x) = |5x – 2|

• gof(x) = g[f(x)]=g|x| = |5|x|-2|.
• fog(x) = f[g(x)] = f(|5x- 2|) =||5x-2|| = |5x – 2|.

(ii) f(x) = 8x³ and g(x) = \(x^{\frac{1}{3}}\)

• gof(x) = g[f(x)] = g(8x³) = (8x³)\(x^{\frac{1}{3}}\) = 2x.
• fog(x) = f[(g(x)] = f(\(x^{\frac{1}{3}}\)) = 8.(\(x^{\frac{1}{3}}\))³ = 8x.