If $$ f(x) = 3x-1$$, $$ n$$ represents the slope of the line with the equation $$ y = f^{-1}(x)$$, and $$p$$ represents the slope of a line that is perpendicular to the line with the equation $$ y=f(x)$$, then $$ np=$$

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Uniteasy Admin · Accepted Answer

From the condition, the slope of $$f(x)=3x-1 $$ is 3.
Since the slopes of inverse functions are reciprocals,  the slope of $$f(x)=3x-1 $$ is $$\dfrac{1}{3} $$, that is
$$n=\dfrac{1}{3}$$
Since the slope of a line that is perpendicular to$$ f(x)$$ is a negative reciprocal of the slope of $$f(x)$$, or $$-\dfrac{1}{3}$$, that is
$$p = -\dfrac{1}{3}$$

The product of $$ n $$ and $$ p$$ is $$-\dfrac{1}{9}  $$

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