Find fog and gof if 1. f(x) – |x| and g(x) – |3x + 4| 2. f(x) = 16x4 and g(x) = x^1/4

Question

Find fog and gof if

1. f(x) – |x| and g(x) – |3x + 4|

2. f(x) = 16x⁴ and g(x) = x^{\(\frac{1}{4}\)}

Answer 1

1. Given;

 f(x) = |x| and g(x) = |3x + 4|

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

= f(|3x + 4|) = ||3x + 4|| = |3x + 4|

gof(x) = g(f(x)) = g(|x|) = |3|x| + 4|

2. fog(x) = f(g(x)) = g(x^1/4) = 16(x^1/4)⁴ = x

gof (x) = g(f(x)) = g(16x⁴) = (16x⁴)^1/4 = 4x.