Question

Hey, Friends
Pls answer all these questions....
Class- 11th ,
Chapter -5
Subject - Maths.....​

Answer 1

The domain and range of the function f(x) = |x - 2| has to be determined. The domain of a function is all values of x for which the value of f(x) is defined. The range of the function is all values of f(x) for values of x that lie in the domain.

The absolute value function f(x) = |x| is defined as f(x) = x for x>=0 and f(x) = -x for x <0.

If f(x) = |x - 2| the value of f(x) is defined for all values of x. The domain of the function is the set of real numbers R. The value of f(x) = |x - 2| is never negative,. For value of x < 2, the function f(x) = 2 - x which is positive. The range of the function is therefore the set [[0, oo)] .

2.

Answer:

Domain: [−3,3]

Range: [−3,0]

Explanation:

In order to find the function's domain, you need to take into account the fact that, for real numbers, you can only take the square root of a positive number.

In other words, in oerder for the function to be defined, you need the expression that's under the square root to be positive.

9−x2≥0

x2≤9⇒|x|≤3

This means that you have

x≥−3 and x≤3

For any value of x outside the interval [−3,3], the expression under the square root will be negative, which means that the function will be undefined. Therefore, the domain of the function will be x∈[−3,3].

Now for the range. For any value of x∈[−3,3], the function will be negative.

The maximum value the expression under the radical can take is for x=0

9−02=9

which means that the minimum value of the function will be

y=−√9=−3

Therefore, the range of the function will be [−3,0].

graph{-sqrt(9-x^2) [-10, 10, -5, 5]}