Relations and Functions — Class 12 Maths Solution

ncert exercise SA NCERT Ex. 1.3,Q.12, Page 19
Question

Let $f:X \to Y$ be an invertible function. Show that the inverse of ${f^{ - 1}}$is $f,$ i.e., ${({f^{ - 1}})^{ - 1}} = f.$

Step-by-step Solution

We know that $f:X \to Y$

As f is invertible $\Rightarrow$ f is one-one and onto $\Rightarrow$ ${f^{ - 1}}$ exists.

Also, ${f^{ - 1}}$is one-one and onto $\Rightarrow$ ${f^{ - 1}}$ is invertible.

$\Rightarrow$ ${({f^{ - 1}})^{ - 1}}$ exists $\Rightarrow$ ${({f^{ - 1}})^{ - 1}} = f$

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NCERT & Exemplar solution for CBSE Class 12 Mathematics, Relations and Functions. Curated by Sachin Sharma. Free for all students.