Given that the function y = f (x) is an odd function defined on R, and f (x) = 2 ^ x when x > 0, try to find the expression of the function y = f (x)

Given that the function y = f (x) is an odd function defined on R, and f (x) = 2 ^ x when x > 0, try to find the expression of the function y = f (x)

Because the function y = f (x) is an odd function defined on R
So f (0) = 0
And when x > 0, f (x) = 2 ^ X
Let x < 0, then - x > 0
So f (- x) = 2 ^ (- x) = 1 / 2 ^ x = - f (x)
So f (x) = - 1 / 2 ^ X
So f (x) = - 1 / 2 ^ x (x < 0)
=0 (x=0)
=2^x (x＞0)

When y = f (x) is known, it is defined as an odd function on R. when x > 0, the expression of y = f (x) is obtained
Given that y = f (x) is an odd function on R, when x > 0, f (x) = the square of X + X-1, find the expression of function y = f (x)

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LZ, you haven't finished your topic, have you

Given that f (x) is an odd function on R, and when x > 0, f (x) = x (1-x), what is the expression of F (x)?

Set x0
f(-x)=-x(1+x)=-f(x)
So when x0, f (x) = x (1-x)

Given that the function FX is an odd function on R, and when x > 0, FX = x (1-x), find the expression of F (x)

When x ﹣ 0, f (x) = x (1 + x),
When x > 0, f (x) = x (1-x),