Find the range of | x-41| /
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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
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