4-Let-f-x-x-2-and-g-x-x-then-find-fog-x-and-gof-x-and-domain-of-fog-x-and-gof-are-they-they-the-same-explain-please-help-me-

Question Number 151804 by abdurehime last updated on 23/Aug/21

4 . Let f (x) = x^{2} and g (x) = \sqrt{x}

then find fog (x) and gof (x) and

domain of (fog) (x) and (gof)

are they they the same ? explain .

please help me ? ? ?

Answered by amin96 last updated on 23/Aug/21

f o g (x) = f (g (x)) = {(\sqrt{x})}^{2} = x

g o f (x) = g (f (x)) = \sqrt{{(x)}^{2}} = x

f o g (x) = g o f (x)

Commented by MJS_new last updated on 23/Aug/21

you are wrong

f (g (- 1)) is not defined \Rightarrow f (g (x)) \neq x

g (f (- 1)) = 1 \neq - 1 \Rightarrow g (f (x)) \neq x

f (g (x)) \neq g (f (x)) \forall x < 0

Answered by MJS_new last updated on 23/Aug/21

f (x) = x^{2} is defined for x \in R

g (x) = \sqrt{x} is defined for x \in R_{0}^{+}

f (g (x)) = {(\sqrt{x})}^{2} = x with x \in R_{0}^{+}

g (f (x)) = \sqrt{x^{2}} =∣ x ∣ with x \in R

Commented by abdurehime last updated on 23/Aug/21

so are they the same or not ? ?

Commented by MJS_new last updated on 23/Aug/21

not .

f (g (x)) is not defined for x < 0

g (f (x)) is defined for x < 0

Commented by abdurehime last updated on 23/Aug/21

thanks let try to question 1 please

Commented by otchereabdullai@gmail.com last updated on 23/Aug/21

nice!