1
AIEEE 2008
+4
-1
Let $$f:N \to Y$$ be a function defined as f(x) = 4x + 3 where
Y = { y $$\in$$ N, y = 4x + 3 for some x $$\in$$ N }.
Show that f is invertible and its inverse is
A
$$g\left( y \right) = {{3y + 4} \over 4}$$
B
$$g\left( y \right) = 4 + {{y + 3} \over 4}$$
C
$$g\left( y \right) = {{y + 3} \over 4}$$
D
$$g\left( y \right) = {{y - 3} \over 4}$$
2
AIEEE 2007
+4
-1
The largest interval lying in $$\left( { - {\pi \over 2},{\pi \over 2}} \right)$$ for which the function

$$f\left( x \right) = {4^{ - {x^2}}} + {\cos ^{ - 1}}\left( {{x \over 2} - 1} \right)$$$$+ \log \left( {\cos x} \right)$$,

is defined, is
A
$$\left[ { - {\pi \over 4},{\pi \over 2}} \right)$$
B
$$\left[ {0,{\pi \over 2}} \right)$$
C
$$\left[ {0,\pi } \right]$$
D
$$\left( { - {\pi \over 2},{\pi \over 2}} \right)$$
3
AIEEE 2005
+4
-1
Let $$f:( - 1,1) \to B$$, be a function defined by
$$f\left( x \right) = {\tan ^{ - 1}}{{2x} \over {1 - {x^2}}}$$,
then $$f$$ is both one-one and onto when B is the interval
A
$$\left( {0,{\pi \over 2}} \right)$$
B
$$\left[ {0,{\pi \over 2}} \right)$$
C
$$\left[ { - {\pi \over 2},{\pi \over 2}} \right]$$
D
$$\left( { - {\pi \over 2},{\pi \over 2}} \right)$$
4
AIEEE 2005
+4
-1
A real valued function f(x) satisfies the functional equation

f(x - y) = f(x)f(y) - f(a - x)f(a + y)

where a is given constant and f(0) = 1, f(2a - x) is equal to
A
- f(x)
B
f(x)
C
f(a) + f(a - x)
D
f(- x)
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