If f (x) is an odd function defined on R, and X ∈ (0, + ∞), f (x) = LG (x + 1), find the expression of F (x) and draw the diagram
① When x = 0, f (0) = 0; ② when x < 0, - x > 0, ∵ f (x) is an odd function, ∵ f (- x) = - f (x) ∵ f (x) = - f (- x) = - LG (- x + 1), to sum up: F (x) = LG (x + 1), (x > 0) 0, (x = 0) − LG (− x + 1), and (x < 0) the image is shown in the following figure:
RELATED INFORMATIONS
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