Let f, g : R → R be defined by f(x)

Question:

Let $f, g: \mathbf{R} \rightarrow \mathbf{R}$ be defined by $f(x)=2 x+\mid$ and $g(x)=x^{2}-2$ for all $x \in \mathbf{R}$, respectively. Then, find gof.

[NCERT EXEMPLAR]

Solution:

We have,

$f, g: \mathbf{R} \rightarrow \mathbf{R}$ are defined by $f(x)=2 x+\mid$ and $g(x)=x^{2}-2$ for all $x \in \mathbf{R}$, respectively

Now,

$g o f(x)=g(f(x))$

$=g(2 x+1)$

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

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

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

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