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JEE MATHEMATICS MCQ: FUNCTIONS

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Analyzing +4 | -1
Let f(x)=x  and  g(x)=∣x∣f\left( x \right) = x\;and\;g\left( x \right) = \left| x \right| for all x∈R.x \in R. Then, the function ϕ(x)\phi \left( x \right) satisfying [ϕ(x)−f(x)]2+[ϕ(x)−g(x)]2=0{\left[ {\phi \left( x \right) - f\left( x \right)} \right]^2} + {\left[ {\phi \left( x \right) - g\left( x \right)} \right]^2} = 0
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Correct option: A
ϕ(x)=x,x∈[0,  ∞)\phi \left( x \right) = x,x \in \left[ {0,\;\infty } \right)
Option A is correct. The given condition implies ϕ(x)=f(x)=g(x)\phi(x) = f(x) = g(x). Since f(x)=xf(x) = x and g(x)=∣x∣g(x) = |x|, this holds only for x≥0x \ge 0, thus ϕ(x)=x\phi(x) = x for x∈[0,∞)x \in [0, \infty).

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