# Function Questions

## What is the formula to find number of one one function ?

Solution : If A and B are two sets having m and n elements respectively such that m $$\le$$ n, then the total number of one-one functions from A to B is $$^nC_m \times m!$$ where m! is m factorial. For example, Let set A have 3 elements and set B have 4 elements, then …

## Find the domain of the function f(x) = $$1\over x + 2$$.

Solution : We have, f(x) = $$1\over x + 2$$ Clearly f(x) assumes real values for all real values for all x except for the values of x satisfying x + 2 = 0  i.e. x = -2. Hence, Domain(f) = R – {-2} Similar Questions If y = 2[x] + 3 & y = …

## If y = 2[x] + 3 & y = 3[x – 2] + 5, then find [x + y] where [.] denotes greatest integer function.

Solution : y = 3[x – 2] + 5 = 3[x] – 1 so 3[x] – 1 = 2[x] + 3 [x] = 4 $$\implies$$ 4 $$\le$$ x < 5 then y = 11 so x + y will lie in the interval [15, 16) so [x + y] = 15 Similar Questions Find the …

## Find the domain and range of function f(x) = $$x-2\over 3-x$$.

Solution : we have,  f(x) = $$x-2\over 3-x$$ Domain of f : Clearly f(x) is defined for all x satisfying 3 – x $$\ne$$ 0 i.e. x $$\ne$$ 3 Hence, Domain of f is R – {3} Range of f : Let y = f(x), i.e.  y = $$x-2\over 3-x$$ $$\implies$$ 3y – xy = …

## Find the period of the function f(x) = $$e^{x-[x]+|cos\pi x|+|cos2\pi x|+ ….. + |cosn\pi x|}$$

Solution : f(x) = $$e^{x-[x]+|cos\pi x|+|cos2\pi x|+ ….. + |cosn\pi x|}$$ Period of x – [x] = 1 Period of $$|cos\pi x|$$ = 1 Period of $$|cos2\pi x|$$ = $$1\over 2$$ ………………………………. Period of $$|cosn\pi x|$$ = $$1\over n$$ So period of f(x) will be L.C.M of all period = 1. Similar Questions If y …

## Find the inverse of the function f(x) = $$log_a(x + \sqrt{(x^2+1)})$$; a > 1 and assuming it to be an onto function.

Solution : Given f(x) = $$log_a(x + \sqrt{(x^2+1)})$$ f'(x) = $$log_ae\over {\sqrt{1+x^2}}$$ > 0 which is strictly increasing functions. Thus, f(x) is injective, given that f(x) is onto. Hence the given function f(x) is invertible. Interchanging x & y $$\implies$$  $$log_a(y + \sqrt{(y^2+1)})$$ = x $$\implies$$  $$y + \sqrt{(y^2+1)}$$ = $$a^x$$ ……..(1) and  $$\sqrt{(y^2+1)}$$ – …

## Find the range of the function $$log_{\sqrt{2}}(2-log_2(16sin^2x+1))$$

Solution : Now 1 $$\le$$ $$16sin^2x$$ + 1) $$\le$$ 17 0 $$\le$$ $$log_2(16sin^2x+1)$$ $$\le$$ $$log_217$$ 2 – $$log_217$$ $$\le$$ 2 – $$log_2(16sin^2x+1)$$ $$\le$$ 2 Now consider 0 < 2 – $$log_2(16sin^2x+1)$$ $$\le$$ 2 -$$\infty$$ < $$log_{\sqrt{2}}(2-log_2(16sin^2x+1))$$ $$\le$$ $$log_{\sqrt{2}}2$$ = 2 the range is (-$$\infty$$, 2] Similar Questions If y = 2[x] + 3 & y …