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It is known that f (x) = the x power of 10 plus the x power of 10 / 10 minus the negative x power of 10, Find its value range
F (x) multiply 10 ^ XF (x) = (10 ^ 2x-1) / (10 ^ 2x + 1) = (10 ^ 2x + 1-2) / (10 ^ 2x + 1) = (10 ^ 2x + 1) / (10 ^ 2x + 1) - 2 / (10 ^ 2x + 1) = 1-2 / (10 ^ 2x + 1) because 10 ^ 2x > 0, the denominator is not 0, so the definition field is RF (x) = 1-2 / (10 ^ 2x + 1) 10 ^ 2x > 010 ^ 2x + 1 > 1, so 0
What is the function f (x) = (3x-1) / (3x + 1)? Function x is the x power of 3, / table divided by
It is an odd function because f (- x) = - f (x). Monotonically increasing
Landlord, if you are not satisfied with my answer, can you ask your question in detail?
F (x) = 3x power + 3x / 1 power - 1 Find (1) prove that f (x) is an odd function (2) judge the monotonicity of F (x) and prove it
F (x) = (3 ^ x-1) / (3 ^ x + 1) f (- x) = (3 ^ (- x) - 1) / (3 ^ (- x) + 1) = (1-3 ^ x) / (1 + 3 ^ x) = - (3 ^ x-1) / (3 ^ x + 1) = - f (x), so it is an odd function. Take x2 > x1f (x2) - f (x1) = (3 ^ x2-1) / (3 ^ x2 + 1) - (3 ^ x1-1) / (3 ^ X1 + 1) = [(3 ^ x2-1) (3 ^ X1 + 1)] / (3 ^ x2 + 1) (
Let f (x) = 3 to the power of X + 3x-8, and use dichotomy to find the x power of equation 3 + 3x-8 = 0 in the process that x belongs to the approximate solution within (1,2) Calculated to f (1) 0f (1.25)
F (1) 0, then the root is (1,1.5)
f(1.5)>0f(1.25)
If the 5th power of (3x + 1) = a × The 5th power of X + B × The fourth power of X + C × The third power of X + D × Power of X + e × X + F, find A-B + C-D + e-f
Expand the 5th power of (3x + 1) = (3x) ^ 5 + C (5,1) (3x) ^ 4 + C (5,2) (3x) ^ 3 + C (5,3) (3x) ^ 2 + C (5,4) (3x) + 1
Corresponding item (3x) ^ 5 = a × The 5th power of X, C (5,1) (3x) ^ 4 = b × The fourth power of X, C (5,2) (3x) ^ 3 = C × The third power of X, C (5,3) (3x) ^ 2 = D × The second power of X, C (5,4) (3x) = e × x,f=1
When x = - 1, the 5th power of (3x + 1) = - A + B-C + D-E + F = (- 2) ^ 5 = - 32
Multiply both sides of - A + B-C + D-E + F = - 32 by - 1 to get A-B + C-D + E-F = 32
Given that 5x + 3 and 3x + 5 are opposite to each other, then the 2009 power of X is () fast
Because they are opposite numbers
So 5x + 3 + 3x + 5 = 0
8x + 8 = 0
x = -1
So the 2009 power of x = (- 1) the 2009 power of x = - 1
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