Question

Find a new function g(x) transformed from f(x)=-x-2 such that g(x) is perpendicular to f(x) .

Answer 1

The new function is g(x) =-1(1/-x) +2.

The transformation of function f(x) to function g(x) is given by g(x)=A f(Bx+ H)+K. where the constant A scales the function vertically. (A negative A reflects the function about the x-axis B scales the function horizontally. (A negative B reflects the function on the y-axis.) H shifts the function horizontally, and K shifts the function vertically.

Convert f(x) to g(x)

where the conversion is g(x)=f(x)+2.

A perpendicular line has negative reciprocal slopes, so for g(x) to be perpendicular to f(x), we need to get the negative reciprocal of -x, which is -1(1/-x)

So, f(x)=-x-2  ; m = -1

From the above information, we get g(x) as follows.

g(x) =-1(1/-x) +2

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