Questions: Find the domain of f(x) = √(-7x+9) Write your answer in interval notation.

Transcript text: Find the domain of $f(x)=\sqrt{-7 x+9}$ Write your answer in interval notation.

Solution

Step 1: Identify the expression under the square root

The expression under the square root is $ax + b$, which is $-7x + 9$.

Step 2: Determine the condition for the expression under the square root to be non-negative

Since the square root of a negative number is not defined in the set of real numbers, we require $-7x + 9 \geq 0$.

Step 3: Solve the inequality

To find the domain, we solve the inequality $-7x + 9 \geq 0$. Given $a = -7$, we solve $x <= \frac{-9}{-7} = 9/7$.

Step 4: Express the solution in interval notation

Based on the solution to the inequality, the domain in interval notation is $(-∞, 9/7]$.

The domain of the function $f(x) = \sqrt{-7x + 9} + 0$ is $(-∞, 9/7]$.

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