iran-konkur 2017 Q119

iran-konkur · Other · konkur-riazi_1396_specialized Tangents, normals and gradients Find tangent line equation at a given point
119. The function $f(x) = x + \ln x$ is defined (given). The equation of the tangent line to the graph of $f^{-1}$ at the point where it meets the bisector of the first quadrant is:
(1) $y + 2x = 3$ (2) $2x - y = 1$ (3) $2x + y = 3$ (4) $2y - x = 1$

120. The $x$-intercept of the normal line to the curve $x^2 + y^2 = 3xy + 3$ at the point $(1, 2)$ is:
(1) $2$ (2) $3$ (3) $4$ (4) $5$
\textbf{119.} The function $f(x) = x + \ln x$ is defined (given). The equation of the tangent line to the graph of $f^{-1}$ at the point where it meets the bisector of the first quadrant is:

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(1) $y + 2x = 3$ \hfill (2) $2x - y = 1$ \hfill (3) $2x + y = 3$ \hfill (4) $2y - x = 1$

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\textbf{120.} The $x$-intercept of the normal line to the curve $x^2 + y^2 = 3xy + 3$ at the point $(1, 2)$ is:

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(1) $2$ \hfill (2) $3$ \hfill (3) $4$ \hfill (4) $5$

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