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Mathematics

Grade10

Easy

Question

Write $straight f left parenthesis straight x right parenthesis space equals space square root of 5 space minus space straight x squared end root$ as the composition of two functions.

$p (x) = 5 - x^{2}, q (x) = \sqrt{x - 1}$
$p (x) = 5 - x^{2}, q (x) = \sqrt{x}$
$p (x) = 5 x^{2}, q (x) = \sqrt{x}$
$p (x) = 5 + x^{2}, q (x) = \sqrt{x}$

hint Hint:

In this question, we have to find $straight f left parenthesis straight x right parenthesis space equals space square root of 5 space minus space straight x squared end root$ as the composition of two functions. A composite function is a function created when one function is used as the input value for another function i.e., a function written inside another function.

The correct answer is: $straight p left parenthesis straight x right parenthesis space equals space 5 space minus space straight x squared space comma space straight q left parenthesis straight x right parenthesis space equals space square root of straight x$

$text Let end text straight p left parenthesis straight x right parenthesis space equals space 5 space minus space straight x squared space comma space straight q left parenthesis straight x right parenthesis space equals space square root of straight x straight q left parenthesis straight p left parenthesis straight x right parenthesis right parenthesis space equals space straight q open parentheses 5 space minus space straight x squared close parentheses space equals space square root of 5 space minus space straight x squared end root$

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