# What is the equation of the line tangent to # f(x)=x^2-sqrt(e^x-3x) # at # x=0#?

See the tangent-inclusive Socratic dented-for-discontinuity graph.

graph{(x^2-sqrt(e^x-3x)-y) [-10, 10, -5, 5]}(x-y-1)(x^2+(y+1)^2-.01)=0

Nearly, for #x in (0.5, 1.5), f is not real. See the graph below, wherein.

graph{y-3x)=00 [0.6 1.5, -5, 5]} = (e^x-y)

f = -1 at x = 1.

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The equation of the line tangent to f(x) = x^2 - sqrt(e^x - 3x) at x = 0 is y = -3x.

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