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Chapter 1: Problem 33

Determine the domain of the function represented by the given equation. $$f(x)=\sqrt{7+x}$$

Short Answer

Expert verified
The domain of the function \(f(x)=\sqrt{7+x}\) is \(x \geq -7\).

Step by step solution

01

Understand the problem

The task is to find the domain of the function \(f(x)=\sqrt{7+x}\). This is the set of input values (x-values) that will not result in a negative number under the square root. The square root of a negative number is undefined in the realm of real numbers.
02

Identify the constraint

The square root function is only defined when its input is greater than or equal to zero. Hence, the quantity under the square root (7+x) must be greater than or equal to zero. This leads to the inequality \(7+x \geq 0\).
03

Solve the inequality

To find the solution, solve the inequality \(7+x \geq 0\) for x by subtracting 7 from both sides. This gives \(x \geq -7\).

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Most popular questions from this chapter

Use interval notation to express the solution set of each inequality. $$|x-1|<9$$

Find a point \(P(x, y)\) on the graph of the equation \(y=x^{2}\) such that the slope of the line through the point (3,9) and \(P\) is \(\frac{15}{2}\)

A boat was purchased for \(\$ 44,000 .\) Assuming the boat depreciates at a rate of \(\$ 4200\) per year (straight-line depreciation) for the first 8 years, write the value \(v\) of the boat as a function of the time \(t\) (measured in years) for \(0 \leq t \leq 8\).

Solve by completing the square or by using the quadratic formula. $$-x^{2}-7 x-1$$

Use the properties of inequalities to solve each inequality. Write answers using interval notation. $$3(x+7) \leq 5(2 x-8)$$
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