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1.Relation and Function
hard
Suppose $f(x) = {(x + 1)^2}$ for $x \ge - 1$. If $g(x)$ is the function whose graph is the reflection of the graph of $f(x)$ with respect to the line $y = x$, then $g(x)$ equals
A
$ - \sqrt x - 1,\;x \ge 0$
B
$\frac{1}{{{{(x + 1)}^2}}},\;x > - 1$
C
$\sqrt {x + 1} ,\;x \ge - 1$
D
$\sqrt x - 1,\;x \ge 0$
(IIT-2002)
Solution
(d) The graph of $f(x)$ has the equation $y = {(x + 1)^2},\,\,x \ge – 1$.
The reflection of the graph
of $f(x)$ is obtained by
interchanging $x,\,y$. So,
the graph of $g(x)$ has the
equation $x = {(y + 1)^2},\,\,y \ge – 1$
$\therefore$ $y = \sqrt x – 1$ because $y \ge – 1$
$\therefore$ $\phi \,(x) = \sqrt x – 1,\,\,\,x \ge 0$.
Standard 12
Mathematics
