It is given that an equation of the tangent line to the graph of y=g(x) at x=9 is

6x+9y=-27.

It follows that y=?                      is the equation of the tangent line to y=g(x^2) at x=3

and that y=?                              is the equation of the tangent line to y=(g(x))^2 at x=9.
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1 Answer

g(9)=g(3²) which is g(x²) when x=3, first answer option.

Furthermore, if we put x=9 in the tangent line equation, we get y=-9, so that the tangent point is (9,-9). Since the y-coord is negative y cannot be (g(x))² for any value of x, because all squares are positive.

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