The x-intercept of the function h(x) is when the function h(x) = 0
The x-intercept of the function is -2
How to determine the x-intercept?
From the question, the function is given as:
[tex]h(x) = 8 * \sqrt[3]{x - 6} + 16[/tex]
Set the function h(x) to 0, to calculate the x-intercept
[tex]8 * \sqrt[3]{x - 6} + 16= 0[/tex]
Subtract 16 from both sides of the equation
[tex]8 * \sqrt[3]{x - 6} +=-16[/tex]
Divide through by 8
[tex]\sqrt[3]{x - 6} =-2[/tex]
Take the cube of both sides
[tex]x - 6 =-8[/tex]
Add 6 to both sides
[tex]x =-2[/tex]
Hence, the x-intercept of the function is -2
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