Class 12 Mathematics - Chapter Relations and Functions NCERT Solutions | Consider f : R → R given by f
Consider f : R → R given by f(x) = 4x + 3. Show that f is invertible. Find the inverse of f.
f: R → R is given by,
f(x) = 4x + 3
One-one:
Let f(x) = f(y).
∴ f is a one-one function.
Onto:
For y ∈ R, let y = 4x + 3.
Therefore, for any y ∈ R, such that
∴ f is onto.
Thus, f is one-one and onto and therefore, f - 1 exists.
Let us define g: R→ R by
.
∴
Hence, f is invertible and the inverse of f is given by
More Questions From Class 12 Mathematics - Chapter Relations and Functions
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(ii) Transitive but neither reflexive nor symmetric.
(iii) Reflexive and symmetric but not transitive.
(iv) Reflexive and transitive but not symmetric.
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(ii) Relation R in the set N of natural numbers defined as
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(iv) Relation R in the set Z of all integers defined as
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(b) R = {(x, y): x and y live in the same locality}
(c) R = {(x, y): x is exactly 7 cm taller than y}
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- Q:- Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as
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- Q:- Show that the relation R in R defined as R = {(a, b): a ≤ b}, is reflexive and transitive but not symmetric.
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