Find (fog)(x) and it’s domain when f(x)=x^2 and g(x)= square root x+5

Question

asked Mar 17, 2023 137k views

1 Answer

Don Hatch · Answer 1 · 2023-03-23T07:40:13+0000

$\quad \huge \quad \quad \boxed{ \tt \:Answer }$

$\qquad \tt \rightarrow \: (fog)(x)= x + 7\: ;\:\: (-∞,∞)$

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$\large \tt Solution \: :$

$\qquad \tt \rightarrow \: f(x) = {x}^(2) + 2$

and

$\qquad \tt \rightarrow \: g(x) = √(x + 5)$

Now,

$\qquad \tt \rightarrow \: (fog)(x) = f(g(x))$

$\qquad \tt \rightarrow \: f(g(x)) = (g(x)) { }^(2) + 2$

$\qquad \tt \rightarrow \: f(g(x)) = ( √(x + 5) ) {}^(2) + 2$

$\qquad \tt \rightarrow \: f(g(x)) = x + 5 + 2$

$\qquad \tt \rightarrow \: f(g(x)) = x + 7$

And here, x can have any real value. because there's no condition where " x + 7 " is not defined and neither it is in indeterminate form.

Therefore, it's domain is All Real. i.e (-∞ , ∞)

Answered by : ❝ AǫᴜᴀWɪᴢ ❞