CAT 2022 Slot 2 Paper

Question : 53 of 66

Marks: +1, -0

Suppose for all integers $x$ , there are two functions $f$ and $g$ such that $f(x) + f(x-1) -1=0$ and $g(x) = x^2$ . If $f(x^2-x)=5$ , then the value of the sum $f (g (5)) + g (f (5))$ is

Your Answer:

Validate

Solution:

Given,

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

f (x^2-x) =5 . . . (ii)

g(x)=x^2

Substituting

x=1

\Eqs (i) \and (ii)

, we get

f(0)=5

f(1)+f(0)=1

f(1)=1-5=-4

f(2)+f(1)=1

f(2)=1+4=5

f(n)=5

n

is even and

f(n)=-4

n

is odd

f(g(5))+g(f(5))=f(25)+g(-4)=-4+16=12

Go to Question:

Prev Question

Next Question