Question

Find the domain and the range of the following real functions (a) f(x) = x+1/x-2​

Answer 1

Answer:

As we are given a real function, thus the domain and range should be real numbers.

(i) f(x)=−∣x∣

f(−1)=−∣−1∣=−1

f(0)=−∣0∣=0

f(1)=−∣1∣=−1

Here, x can be any real number, but f(x) will always be negative or zero.

Therefore,

Domain of function =R(All real numbers)

Range of the function = Negative real numbers

(ii) f(x)=

9−x

2

9−x

2

≥0

x

2

<9

x<±3

x∈[−3,3]

f(−3)=

9−(−3)

2

=0 (Real number)

f(0)=

9−0

=3 (Real number)

f(3)=

9−(3)

=0 (Real number)

Here,

−3≤x≤3

0≤f(x)≤3

Therefore,

Domain of function =[−3,3]

Range of the function =[0,3]