Consider `f" ":" "{1," "2," "3}->{a ," "b ," "c}` given by `f(1)" "=" "a` , `f(2)" "=" "b` and `f(3)" "=" "c` . Find `f^(-1)` and show that `(f^(-1))^(-1)=" "f` .

Let f" ":" "{1," "2," "3}->{a ," "b ," "c} be one-one and onto function given by f" "(1)" "=" "a , f" "(2)" "=" "b and f" "(3)" "=" "c . Show that there exists a function g" ":" "{a ," "b ," "c}->{1," "2," "3} such that gof=I_x and fog=

If f(y) = 2y^(2) + by + c and f(0) = 3 and f(2) = 1, then the value of f(1) is

Let f : R rarr given by f(x) = 3x^(2) + 5x + 1 . Find f(0), f(1), f(2).

If f: C->C is defined by f(x)=(x-2)^3 , write f^(-1)(-1) .

Consider as f(1)=a,f(2)=b,f(3)=c , g:[a,b,c]rarr {apple, ball, cat} Defined as f(1)=a,f(2)=b,f(3)=c, g(a) = apple, g(b) = ball, g(c ) = cat Show that f, g and gof are invertible. Find f^(-1),g^(-1) and (gof)^(-1) and show that : (gof)^(-1)=f^(-1)og^(-1) .

Let S" "=" "{1," "2," "3} . Determine whether the functions f" ":" "S->S defined as below have inverses. Find f^(-1) , if it exists. (a) f" "=" "{(1," "1)," "(2," "2)," "(3," "3)} (b) f" "=" "{(1," "2)," "(2," "1)," "(3," "1)} (c) f" "=" "

Let S" "=" "{a ," "b ," "c}" "a n d" "T" "=" "{1," "2," "3} . Find F^(-1) of the following functions F from S to T, if it exists. (i )" "F" "=" "{(a ," "3)," "(b ," "2)," "(c ," "1)} (ii) F" "=" "{(a ," "2)," "(b ," "1)," "(c ," "1)}

If f(x) = ax^2 + bx + c and f(0) = 5 , f(1) = 7 , and f(-1) = 3 then find the value of 3a+5b-c .

If the function f: C->C be defined by f(x)=x^2-1 , find f^(-1)(-5) and f^(-1)(8) .

f(x)=(2x+3)/(3x+2), then show that f(x)*f((1)/(x))=1. if f(x)=4, then show that f(x+1)-f(x)=f(x)