Question

If f and g are two increasing functions such that fog is defined, then-

• A. Fog is an increasing function
• B. Fog is a decreasing function
• C. Fog is neither increasing nor decreasing
• D. None of these

Answer 1

Answer: (A)

Fog is an increasing function

Answer 2

Let x₁, x₂ Î R such that x₁ < x₂. Then, x₁ < x₂

̃ f(x₁) < f(x₂) [Q f is an increasing function]

̃ g (f(x₁)) < g(f(x₂)) [Q g is an increasing

function]

̃ gof (x₁) < gof (x₂)

Hence gof is an increasing function.