   Chapter 2.5, Problem 73E

Chapter
Section
Textbook Problem

Let f ( x ) = { x + 2 if  x ≤ 1 k x 2 if  x > 1 Find the value of k that will make f continuous on (−∞, ∞).

To determine
The value of k at which the given function is continuous on (,) .

Explanation

Given information:

The given function is f(x)={x+2ifx1kx2ifx>1 .

Definition used:

The function will be continuous when the value of left hand limit and the value of right hand limit is equal to the value of the function at that point and value of that function should satisfy that point.

A function f is continuous at x=a when it follows the following three conditions,

(1) f(a) is defined.

(2) limxaf(x) exists.

(3) limxaf(x)=f(a) .

Calculation:

The given function is,

f(x)={x+2ifx1kx2ifx>1

Calculate the value of the function f(x) at x=1 .

Substitute 1 for x in the given function

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