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Q.
A function $f$ has domain $[-1,2]$ and range $[0,1]$. The domain and range respectively of the function $g$ defined by $g(x)=1-f(x+1)$ is
Relations and Functions - Part 2
Solution:
func/sc $g(x)$ is defined if $f(x+1)$ is defined.
Hence the domain of $g$ is all $x$ such that $(x+1) \in[0,2]$
i.e. $-1 \leq(x+1) \leq 2 $
$\Rightarrow -2 \leq x \leq 1 $ (domain of $g$ )
again $f ( x +1) \in[0,1]$
$\therefore - f ( x +1) \in[-1,0] $
$ 1- f ( x +1) \in[0,1]$
which is the range of $g$. ]