Given that f(x) = (√(1−x)) Find a) D_f for the arranged form of f(x) b) fg if fh= g(x) and h(x)= 3x^2 −4 c) A(x)= { (((√(1−x)) , x≠ 1)),((x^2 ,x≠0)) :} find A^(−1) .


Question and Answers Forum

All Questions Topic List
None Questions
Previous in All Question Next in All Question
Previous in None Next in None
Question Number 42730 by Rio Michael last updated on 01/Sep/18
$Given that f(x) = (√(1−x)) Find a) D_f for the arranged form of f(x) b) fg if fh= g(x) and h(x)= 3x^2 −4 c) A(x)= { (((√(1−x)) , x≠ 1)),((x^2 ,x≠0)) :} find A^(−1) .$
$G i v e n t h a t f (x) = \sqrt{1 - x} F i n d$ $a) D_{f} f o r t h e a r r a n g e d f o r m o f f (x)$ $b) f g i f f h = g (x) a n d h (x) = 3 x^{2} - 4$ $c) A (x) = {\begin{cases} \sqrt{1 - x}, x \neq 1 \\ x^{2}, x \neq 0 \end{cases}$ $f i n d A^{- 1} .$
Commented by Joel578 last updated on 03/Sep/18

$For (c)$ $if x = - 1, what function A (x) should be defined ?$ $A (x) = \sqrt{1 - x} or A (x) = x^{2} ?$
	Answered by Joel578 last updated on 02/Sep/18
	$(a) D_f = {x ∈ R : x ≤ 1 } (b) (f . h)(x) = (3x^2 − 4)(√(1−x)) = g(x) (f . g)(x) = ((√(1 − x)))^2 (3x^2 − 4) = (1 − x)(3x^2 − 4) = −3x^3 + 3x^2 + 4x − 4$
	$(a)$ $D_{f} = {x \in R : x ⩽ 1}$ $(b)$ $(f . h) (x) = (3 x^{2} - 4) \sqrt{1 - x} = g (x)$ $(f . g) (x) = {(\sqrt{1 - x})}^{2} (3 x^{2} - 4)$ $= (1 - x) (3 x^{2} - 4)$ $= - 3 x^{3} + 3 x^{2} + 4 x - 4$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum