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Question

A function f:RR is defined by f(x)=x2. Determine.
i) Range of f
ii) {x:f(x)=4}
iii) {y:f(y)=1}


Solution

We have,
f(x)=x2(i)
(i) Clearly range of f=R+ (set of all real numbers greater than or equal to zero)

(ii) We have,
{x:f(x)=4}f(x)=4(ii)
Using equation (i) and equation (ii), we get
x2=4x=±2{x:f(x)=4}={2,3}

(iii) {y:f(y)=1}
f(y)=1(i)
Clearly, x21 or x20
f(y)1
{y:f(y)=1}=ϕ


Mathematics
RD Sharma
Standard XI

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