what is the domain of $f(x)=5^{x}-7$?\n{$x|x > - 7$}\n{$x|x < - 7$}\n{$x|x > 0$}\n{$x|x$ is a real number}
what is the domain of $f(x)=5^{x}-7$?\n{$x|x > - 7$}\n{$x|x < - 7$}\n{$x|x > 0$}\n{$x|x$ is a real number}
Answer
Explanation:
Step1: Recall exponential - function properties
The function $y = a^x$ ($a>0,a\neq1$) is defined for all real - valued $x$. Here, $a = 5$ in the function $y = 5^x$.
Step2: Consider the given function
The function $f(x)=5^x - 7$ is a transformation of the exponential function $y = 5^x$ (a vertical shift down by 7 units). Since $5^x$ is defined for all real $x$, $f(x)=5^x - 7$ is also defined for all real $x$.
Answer:
D. ${x|x\text{ is a real number}}$