If a non-zero function $f$ satisfies the relation $f (x + y) + f (x - y) = 2 f (x) . f (y)$ for all $x, y$ in $R$ and $f (0) \neq 0$ ; then $f (10) - f (- 10) =$

Q. For all non - negative integers x and y, f(x,y) is defined as below.
f(0, y) = y + 1
f(x + 1, 0) = f(x, 1)
f(x + 1, y + 1) = f(x, f(x + 1, y)) find f(1, 2)?

Q. If

y = f (x)

be a function satisfying the relation

y^{2} - x^{2} y = x

, then which of the following may hold good for

y = f (x)

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Let f(x,y) be a function satisfying the relation f(x,0)=x and f(x,y+1)=f(f(x,y),y) for all non-negative integers. Then which of the following is the largest?

The correct option is A f(15,20)f(x,1)=f(f(x,0),0)=f(x,0)=x f(x,2)=f(f(x,1),1)=f(x,1)=x ⋮ f(x,y)=x ∀ y≥0 ∴ Option (a) is correct.

Let $f (x, y)$ be a function satisfying the relation $f (x, 0) = x$ and $f (x, y + 1) = f (f (x, y), y)$ for all non-negative integers. Then which of the following is the largest?

The correct option is A $f (15, 20)$
$f (x, 1) = f (f (x, 0), 0) = f (x, 0) = x$
$f (x, 2) = f (f (x, 1), 1) = f (x, 1) = x$
$⋮$
$f (x, y) = x \forall y \geq 0$
$∴$ Option (a) is correct.