A function f(x) is defined as f(x) = 
. If functions g(x), h(x) and φ (x) are defined as g(x) = f(x), h(x) = f(–x) and φ (x) = – f(– x), then
(i) If F(x) = max [f(x), g(x)], then F(x) =
Text Solution
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Ans.
(i)
Sol.
So, F(x) = | f(x) | ⇒
f(x) = g(x) ⇒ x = 0
Hence number of +ve integral values of x is zero ⇒
φ (x) = – f(–x) = f(x)
h(x) = g(x), so f(x) + h(x) = 0
Hence false statement is g(x) = φ (x) ⇒
(ii)
Sol.
So, F(x) = | f(x) | ⇒
f(x) = g(x) ⇒ x = 0
Hence number of +ve integral values of x is zero ⇒
φ (x) = – f(–x) = f(x)
h(x) = g(x), so f(x) + h(x) = 0
Hence false statement is g(x) = φ (x) ⇒
(iii)
Sol.
So, F(x) = | f(x) | ⇒
f(x) = g(x) ⇒ x = 0
Hence number of +ve integral values of x is zero ⇒
φ (x) = – f(–x) = f(x)
h(x) = g(x), so f(x) + h(x) = 0
Hence false statement is g(x) = φ (x) ⇒
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