Question

Find the range of | x-41| /
X-4​

Answer 1

Answer:

ANSWER

(i) Given x>0

⇒3x>0

⇒−3x<0

⇒2−3x<2

⇒f(x)<2

∴ Range of f=(−∞,2)

(ii) Since, for any real number x, x

2

≥0

⇒x

2

+2≥0+2

⇒x

2

+2≥2

⇒f(x)≥2

∴ Range of f=[2,∞)

(iii) f(x)=x,x is a real number

It is clear that the range of f is the set of all real numbers

∴ Range of f=RANSWER

(i) Given x>0

⇒3x>0

⇒−3x<0

⇒2−3x<2

⇒f(x)<2

∴ Range of f=(−∞,2)

(ii) Since, for any real number x, x

2

≥0

⇒x

2

+2≥0+2

⇒x

2

+2≥2

⇒f(x)≥2

∴ Range of f=[2,∞)

(iii) f(x)=x,x is a real number

It is clear that the range of f is the set of all real numbers

∴ Range of f=R