If `A={2, 3, 4, 5}` then which of the following relation is a function from A to itself ?
i) `f_(1)={(x, y):y=x+1}`
ii) `f_(2)={(x, y):x+ygt6}`
iii) `f_(3)={(x, y):yltx}iv)f_(4)={(x, y):x+y=7}`

Examples :- If x,y in {1;2;3;4} ;then which of the following are function in the given set ? (a) f_1={(x;y):y=(x+1)} (b) f_2={(x;y):x+y>4} (c) f_3={(x,y):y

If A={1,2,3,4} . Prove that f defined by f={(x,y) , x+y=5} is function from A to A

If the square ABCD, where A(0,0),B(2,0)C(2,2) and D(0,2) undergoes the following three transformations successively (i) f_(1)(x,y) to (y,x) (ii) f_(2)(x,y) to (x+3y,y) (iii) f_(3) (x,y) to ((x-y)/2,(x+y)/2) then the final figure is a

If f(x)=a^(x), which of the following equalities do not hold ? ( i )f(x+2)-2f(x+1)+f(x)=(a-1)^(2)f(x) (ii) f(-x)f(x)-1=0 (iii) f(x+y)=f(x)f(y)( iv )f(x+3)-2f(x+2)+f(x+1)=(a-2)^(2)f(x+1)

Express each relation in the form of ordered pair and check whether is it a function or not? (i) f={(x,y): y=3x, x in {1,2,3}, y in {3,6,9,12}} (ii) g={(x,y): y gt x + 1 , x in {1,2}, y in {2,4,6}} (iii) h={(x,y): x+y=3,x,y in {0,1,2,3}}

If 2x+3|y|=4y, then y as a function of x i.e.y=f(x), is -

Find dervatives of the following functions: (i) y=2x^(3) , (ii) y=4/x , (iii) y=3e^(x) , (iv) y=6 ln x , (v) y=5 sin x

If f:R rarr R is a function such that f(x)=2^(x), find.(i) range of f( ii) (x:f(x)=1) (iii) f(x+y)=f(x)+f(y) is true or false.

If f(x)=sin(pi x), then draw the graph of the followings :(i)y=f(|x|)( ii) y=f(-|x|) (iii) |y|=f(x)