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The inverse function of the function f (x) = 2 ^ - x (x > 0) f ^ - 1 (x) =? A. - log base 2 true x (x > 0) B. - log base 2 true (- x) (x < 0) C Inverse function f ^ - 1 (x) =? 2 ^ - x (x ＞ 0)? A. - log base 2 true x (x > 0) B. - log base 2 true (- x) (x < 0) C. - log base 2 true x (0 < x < 1) D. - log base 2 true (- x) (- 1 < x < 0)
y=f(x)=2^(-x)
log2(y)=-x
x=-log2(y)
X>0
-x
Find the inverse function of the function f (x) = log (1 + 1 / x) (x > 0) As the title
What is the base number? If y = LG (1 + 1 / x), 10 ^ y = 1 + 1 / x 1 / x = 10 ^ Y-1 swap X and y to get y = 1 / (10 ^ x-1)
Can you understand? Is this what you're asking for?
Function y = 2x + A and function y = BX-1 / 2 are inverse functions of each other, and the values of a and B are calculated
Swap X and y of the first one and substitute it for the second function
Thus, y = B (2Y + a) - 1 / 2 = 2by + AB-1 / 2 is obtained
So 2B = 1, AB-1 / 2 = 0
Thus a = 1, B = 1 / 2
Find the inverse function of F (x) = 3x + 2 / 2x-1 Don't forget to define the domain
0
0
∵y=3x/(2x-1)
∴（2x-1)y=3x
2yx-y=3x
(2y-3)x=y
x=y/(2y-3)
The inverse function of F (x) is x / (2x-3) (x ≠ 3 / 2)
Given that f (x) = 2x / 1 + 3x, the inverse function of y = [inverse function of F (x + 4)] is?
y=f(x+4)=2(x+4)/[1+3(x+4)]=(2x+8)/(3x+13)
2x+8=(3x+13)y
2x+8-3xy-13y=0
(2-3y)x=13y-8
x=(13y-8)/(2-3y)
The inverse function of the inverse function of F (x + 4) is y = (13x-8) / (2-3x) [x, y exchange]
If the inverse function of function y = 3x-2 / 4x + m is itself, Let f (x) = 2x + 3 G (x + 2) = f (x) find g (x) If y = f (x) is a function whose domain is r, then the line x = a has several intersections with the function image
1. If the inverse function of function y = (3x-2) / (4x + m) is itself, find M solution: from y = (3x-2) / (4x + m), 4xy-3x + my + 2 = 0, because its inverse function is itself, X and y are interchangeable, and the equation remains unchanged, M = - 3.2. Let f (x) = 2x + 3, G (x + 2) = f (x) find g (x) g (x) = f (X-2) = 2 (X-2) + 3 = 2x-1
If y = 1 / 2x + A and y = 3-bx are inverse functions of each other, then what are the values of a and B
y=1/2x+a.x=2y-2a;y=3-bx
-b=2;3=-2a
b=-2,a=-1.5
It is known that y = 2x + A and y = 4-bx are inverse functions of each other. Find the values of a and B
y=2x+a
2x=y-a
x=y/2-a/2
So the inverse function y = x / 2-A / 2 and y = 4-bx are the same function
So - B = 1 / 2, - A / 2 = 4
b=-1/2,a=-8
Let f (x) = (X-2) / (AX-1) (a is not equal to 0) have inverse function. It is proved that the image of y = f (x) is symmetric with respect to the line y = X How to prove it,
In the past, we measured and tested the data of the first year of senior high school. We set the point x0 f (XO) and calculated its inverse function. The vertical bisector between F (x0) x0 and XO f (x0) is y = X
It's stupid, but if you don't, it's wrong
RELATED INFORMATIONS
- 1. If the symmetric center of the inverse function image of the function f (x) = (A-X) / (x-a-1) is (- 1,4), then the real number a =? Isn't the original function over (4,
- 2. It is proved that the inverse function of the function y = (1-x) / (1 + x) (x is not equal to - 1) is the function itself
- 3. It is known that the function y = f (x) has the value of inverse function in its definition domain (- ∞, 1), f (x) = x ^ 2-2x, f ^ - 1 (- 1 / 2)
- 4. What is the coordinates of the intersection point between the image of the inverse function of F (x) = log3 (x + 3) and the Y axis?
- 5. 0
- 6. Given that the inverse function g (x) of the function f (x) = 2x satisfies g (a) g (b) = 4, find the minimum value of 1 part of a and 1 part of B
- 7. Given that x satisfies 8 ≤ x ≤ 32, find the maximum and minimum values of the function f (x) = log2x / 8 · (log2x-1)
- 8. Let x satisfy inequality 2 (Log1) 2x)2+7log1 2X + 3 ≤ 0, find the function f (x) = (log2x) 4)(log2x 2) Maximum and minimum values of
- 9. Why do we need to find the range of the original function when we find the inverse function of a function
- 10. What is the inverse function of F (x) = (x + 1) inx-x + 1?
- 11. We know that the quadratic function f (x) = ax ^ 2 + BX + C (a, B are constants and a is not equal to 0), the condition is satisfied: F (0) = f (2) = 0 and the equation f (x) = 2x has two equal roots 1: Find the analytic formula of F (x) 2: Try to determine an interval P such that f (x) decreases monotonically in P and the inequality f (x) ≥ 0 holds in P 3: Ask whether there is a real number m, n (m)
- 12. The function f (x) = 1 + log the logarithm of X (a > 0, a is not equal to 0) with the function f (x) = 1 + log, If point a is on the line MX + NY-2 = 0, where Mn > 0, then the minimum value of 1 / M + 1 / N is obtained
- 13. 0
- 14. Given that the inverse function of the function y = f (x) is y = F-1 (x), then the expression of the inverse function of the function y = 2F-1 (3x + 4)
- 15. The inverse function of the function y = ln (x + √ (x 2 + 1)),
- 16. Given that the square of X - 3x + 2 is equal to 0,6x - (the square of 2x) is equal to what
- 17. If the inverse function of y = negative root minus x square is itself, then the definition domain of the original function is
- 18. Why is the inverse function of the function y = log with 2 as the base and X + 1 as the X power-1 of y = 2 Why is the inverse function of the logarithm of y = log base 2 x + 1 be y = 2 X-1
- 19. Is the inverse function of x = y?
- 20. If the image of function f (x) passes through a straight line of point (4, - 1) and the image of its inverse function passes through the point (- 3, - 2), then the analytic formula of function f (x) is The inverse function of the function f (x) = 4-x ^ 2 (- 2 < = x < = 0) is The inverse function of the function y = 2 ^ x + 1 (x > = 0) is Please explain in detail!