which statement is true about the function $f(x)=-sqrt{x}$?\nit has the same domain and range as the…
which statement is true about the function $f(x)=-sqrt{x}$?\nit has the same domain and range as the function $f(x)=sqrt{x}$.\nit has the same range but not the same domain as the function $f(x)=sqrt{x}$.\nit has the same domain and range as the function $f(x)=-sqrt{-x}$.\nit has the same range but not the same domain as the function $f(x)=-sqrt{-x}$.
Answer
Explanation:
Step1: Encontrar el dominio de $f(x)=-\sqrt{x}$
El argumento de la raíz cuadrada debe ser no - negativo. Entonces, $x\geq0$. El dominio es $[0,+\infty)$.
Step2: Encontrar el rango de $f(x)=-\sqrt{x}$
Como $\sqrt{x}\geq0$, entonces $-\sqrt{x}\leq0$. El rango es $(-\infty,0]$.
Step3: Analizar el dominio y rango de $f(x)=\sqrt{x}$
El dominio de $f(x)=\sqrt{x}$ es $x\geq0$ (dominio $[0,+\infty)$) y el rango es $y\geq0$ (rango $[0,+\infty)$).
Step4: Analizar el dominio y rango de $f(x)=-\sqrt{-x}$
Para el dominio, $-x\geq0$, es decir $x\leq0$ (dominio $(-\infty,0]$). Y $-\sqrt{-x}\leq0$ (rango $(-\infty,0]$).
Answer:
It has the same range but not the same domain as the function $f(x)=-\sqrt{-x}$.