How do you find the domain of $F (x) = x + 7$ $F(x)=x+7$ if $x \leq 4$ $x<=4$ and $x^{2}$ $x^2$ if x > 4?

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Answer 1 · 2015-04-14T15:03:01

You have allready given the domains by giving the limits on $x$ $x$
Probably you meant range .

(1)
$f (x) = x + 7$ $f(x)=x+7$ has a range where you put in any value $x \leq 4$ $x<=4$

So range of $f (x) \leq 4 + 7 = 11 \to$ $f(x)<=4+7=11->$
$- \infty < f (x) \leq 11$ $-oo < f(x)<=11$

(2)
If $x > 4$ $x>4$ then $x^{2} > 4^{2} \to x^{2} > 16$ $x^2>4^2->x^2>16$

So the range is $16 < f (x) < \infty$ $16 < f(x) < oo$

How do you find the domain of F(x)=x+7F(x)=x+7F(x)=x+7 if x<=4x≤4x<=4 and x^2x2x^2 if x > 4?