f(x)=1-h(x),g(x)=1-k(x),h(x)=f(x)+1 f(x)=g(x)+1,k(x)=f(x)+1 Find the value of \frac{j(f(x))+k(h(x))}{h(k(x))+f(j(x))}

CAT 2017 Quantitative Ability

Question : 12 of 34

Marks: +1, -0

f(x)=1-h(x),g(x)=1-k(x),h(x)=f(x)+1

f(x)=g(x)+1,k(x)=f(x)+1

Find the value of

{j(f(x))+k(h(x))}/{h(k(x))+f(j(x))}

Solution:

f(x) = 1 - h(x) ....(i)

g(x) = 1 - k(x) ......(ii)

h(x) = f(x) + 1 ...... (iii)

j(x) = g(x) + 1 ......(iv)

k(x) = j(x) + 1 .......(v)

From Eqs. (i) and (iii), we get

f(x) + h(x) = 1 - h(x) + f(x) + 1

⇒ h(x) = 1 .....(vi)

⇒ f(x) = 0 .....(vii)

From Eqs. (ii) and (iv), we get

g(x) = 1 - k(x) = 1 - (j(x) + 1)

g(x) = -j(x) ......(viii)

From Eqs. (iv) and (viii), we get

j(x) - g(x) = 1

and

g(x) = -j(x)

⇒ j(x) = 1/2 .....(ix)

∴ g(x) = -1/2 ......(x)

∴ k(x) = j(x) + 1 = 3/2 ......(xi)

Hence , f(x) = 0

g(x) = -1/2

h(x) = 1

j(x) = 1/2

k(x) = 3/2

Thus all the functions are constant

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