k(x) is a function such that k(f(x)) = a + b + c + d, where
a = 
b = 
c = 
d = 
A = {x 2 , e x , sinx, | x |} all functions in set A are defined from R to R
B = {18, 19, 16, 17}
h : R → R; h(x) = 
and
φ : 
→ R ; φ (x) = tanx
(i) k( φ (x)) is equal to
Text Solution
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Ans.
(i)
Sol. φ : 
→ R ; φ (x) = tanx
is one-one, odd, non-periodic and onto function hence k( φ( x)) = – 1 + 4 + 5 + 7 = 15
(ii)
Sol. h : R → R, h(x) = 
is even, non-periodic, many one and into function so k(h(x)) = 0 + 4 + 6 + 8 = 18
(iii)
Sol. For f(x) = x 2 , k(f(x)) = 0 + 4 + 6 + 8 + 18
f(x) = e x k(f(x)) = 2 + 4 + 5 + 8 = 19
f(x) = sinx k(f(x)) = –1 + 3 + 6 + 8 = 16
f(x) = | x | k(f(x)) = 0 + 4 + 6 + 8 = 18
So k(x) is many one into
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