Question

Over what part of the domain is function f increasing ?

Answer 1

Step 1: Define increasing function.

A function, f, is said to be increasing if

$\begin{gathered} f(x_2)\ge f(x_1) \\ \text{where} \\ x_2\text{ and }x_1\text{ are in the domain of }f\text{ such that} \\ x_2\ge x_1 \end{gathered}$

Step 2: Check if the given function is increasing in the domain (-∞,-1).

Let x₁ and x₂ be members of the domain such that x₂ ≥ x₁.

Then, we have

$x_2+3\ge x_1+3$

Since,

$f(x)=x+3,\text{for }x<-1$

then,

$f(x_2)=x_2+3\ge x_1+3=f(x_1)$

Therefore, the function is increasing for all x such that x < -1