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Which of the following is true for the relation f(x) = x2 + 8? Only the inverse is a function. Both the equation and its inverse are functions. Only the equation is a function. Neither the equation nor its inverse is a function.

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ANSWER

Only the equation is a function

EXPLANATION

[tex]f(x)=x^2+8[/tex] is graphed above with its inverse [tex]f^{-1}(x)=\pm \sqrt{x-8}[/tex].


We perform the vertical line test for both the equation and its inverse.


The equation [tex]f(x)=x^2+8[/tex] passed the vertical line hence it is a function.

However, [tex]f^{-1}(x)=\pm \sqrt{x-8}[/tex] failed the vertical line test, hence it is not a function.


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