Questions: Solve the problem. f(x) = √(x + 3) a. Graph f(x) b. Write an equation for f⁻¹(x) c. Write the domain of f⁻¹ in interval notation

Graph \( f(x) = \sqrt{x+3} \)

Identify the function

The function to graph is \( f(x) = \sqrt{x+3} \).

Determine the domain

The domain of \( f(x) = \sqrt{x+3} \) is \( x \geq -3 \).

Determine the range

The range of \( f(x) = \sqrt{x+3} \) is \( y \geq 0 \).

\(\boxed{\text{Graph of } f(x) = \sqrt{x+3} \text{ is plotted.}}\)

Write an equation for \( f^{-1}(x) \)

Express \( y = f(x) \)

Let \( y = \sqrt{x+3} \).

Solve for \( x \) in terms of \( y \)

Square both sides: \( y^2 = x + 3 \).

Isolate \( x \)

\( x = y^2 - 3 \).

Express \( f^{-1}(x) \)

Thus, \( f^{-1}(x) = x^2 - 3 \).

\(\boxed{f^{-1}(x) = x^2 - 3}\)

Write the domain of \( f^{-1} \) in interval notation

Determine the domain of \( f^{-1}(x) \)

The domain of \( f^{-1}(x) = x^2 - 3 \) is all real numbers, \((-\infty, \infty)\).

\(\boxed{(-\infty, \infty)}\)

\(\boxed{\text{Graph of } f(x) = \sqrt{x+3} \text{ is plotted.}}\) \(\boxed{f^{-1}(x) = x^2 - 3}\) \(\boxed{(-\infty, \infty)}\)

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