Class XII ISC Maths Chapter Relation and Functions Exercise 1.5
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class 12 relation&function exercise1-1
Relations & Functions
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Q1 Let f : {1, 2, 3} ->{a,b, c) be a function defined by f(1)=a, f(2)=b and f(3) = c. Show that f is invertible and find f-1 Also show that (f-1)-1=f
Q2 Let S = {1, 2, 3} Determine whether the functions f:S->S defined as below have inverse. Find f-1, if it exists. - f={(1, 1), (2, 2), (3, 3)}
- f={(1, 2),(2,1),(3,1)}
- f = {(1, 3), (3, 2), (2, 1)}
- f = {(1, 3),(2,2),(3,1)}
Q3 Explain why the following functions f : X-> Y do not have inverses : - X = R - {0}, Y= R and f(x) = 1/x for all x∈X.
- X = {-1, 0, 1, 2}, Y = {2, 3} and f (x) = 2 for x = -1, 0, 1 and f (2) = 3
- X = R=Y and f(x) = x2 + 1 for all x∈R
Q4 Let S = {a, b, c} and T = {1, 2, 3} Find f-1 of the following functions f from S to T, if it exists. - f = {(a, 3), (b, 2), (c, 1)}
- f = {(a, 2), (b, 1) (c, 1)}
Q5 Let R be the set of all real numbers. Show that the function f : R-> R defined by f (x) = 4x + 5 is invertible. Also find inverse of f.
Q6 Show that the function f : R-> R defined by = 2x-1/3 is one-one and onto. Also find the inverse of the function f.
Q7 If A = R -{-3} and B = R - {2} and a function f: A --> B be given by f(x) =2x-1/x+3,then show that the function f is one-one and onto. Hence, find f-1
Q8 Consider the function f :R+-> [9,∞) defined by f (x) = x2 + 9, where R+ is the set of all non-negative real numbers. Show that f is inversible. Also find the inverse of f
Q9 If Ro is the set of all non-zero real numbers, show that the function f : Ro-->Ro defined by f (x) = 3/x is invertible and it is the inverse of itself
Q10 Let f:N-->S be a function defined by f(x) = 9x2 + 6x - 5, where S is the range of. Show that f is inversible. Find the inverse of f and hence find f-1(43) and f-1 (163).
Q11 If function f : R-->R is defined by f (x) = 5x - 3, then find function g : R -->R such that gof = IR = fog.
Q14 If f : R-->R is a function defined by f(x) = 3x-2/5 is inversible,find the inverse of f
Q18 If f : R - {-3/5} --> R is a function defined by f (x)=2x/5x+3,then find f-1:range of f -->R -{-3/5}
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