Find the​ x-intercept(s) algebraically.

Question

​f(x)equals9 x squared minus 81
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Part 1
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​(Type an exact​ answer, using radicals needed. Use integers or fractions for any numbers in the expression. Type each solution only once

Answer 1

To find the x-intercept(s) of the function \( f(x) = 9x^2 - 81 \), we need to set \( f(x) \) equal to zero and solve for \( x \):

\[ 9x^2 - 81 = 0 \]

Next, we can add 81 to both sides:

\[ 9x^2 = 81 \]

Now, divide both sides by 9:

\[ x^2 = 9 \]

Now, take the square root of both sides:

\[ x = \pm 3 \]

Thus, the x-intercepts of the function are:

\[ x = 3 \quad \text{and} \quad x = -3 \]

In conclusion, the x-intercepts are:

\[ x = 3 \quad \text{and} \quad x = -3 \]