If f,g:R R be defined by f(x) = 2x + 1 and g(x) = x 2 - 2, x R respectively. Then, find gof

It is given that,, f(x) = 2x + 1 and g(x) = x 2 - 2, x R gof = g f(x) = g(2x + 1) = (2x + 1) 2 - 2 = 4 x 2 + 4x + 1 - 2 = 4 x 2 + 4x - 1

Relations and Functions — Class 12 Maths Solution

exemplar sa SA NCERT Exemp.Q.3,Page 11

Question

If $f,g:R \to R$ be defined by $f(x) = 2x + 1$ and $g(x) = {x^2} - 2,\forall x \in R$
respectively. Then, find $gof$

Step-by-step Solution

It is given that,, $f(x) = 2x + 1$ and $g(x) = {x^2} - 2,\forall x \in R$

$\therefore$ $gof = g\{ f(x)\}$

$= g(2x + 1) = {(2x + 1)^2} - 2$

$= 4{x^2} + 4x + 1 - 2$

$= 4{x^2} + 4x - 1$

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