If $f:R \rightarrow R$ and $g:R \rightarrow R$ are defined by $f(x) = x - 3$ and $g(x) = x^{2} + 1$, then the values of $x$ for which $g\left\{ f(x) \right\} = 10$ are

Question

Dr. Abubacker · Accepted Answer

(d)
Given, $f(x) = x - 3,\ \ g(x) = x^{2} + 1$
$	herefore\ \ \ \ \ \ \ g\left\{ f(x) ight\} = g(x - 3)$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 10 = (x - 3)^{2} + 1$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 10 = x^{2} + 10 - 6x$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ x(x - 6) = 0 \Rightarrow x = 0,\ 6$

Q. If $f:R \rightarrow R$ and $g:R \rightarrow R$ are defined by $f(x) = x - 3$ and $g(x) = x^{2} + 1$, then the values of $x$ for which $g\left\{ f(x) \right\} = 10$ are

Explanation

Reviewed by Dr. Abubacker

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