![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
How to find the inverse function of y = 3x / (3x + 1)
The definition field x ≠ - 1 / 3, the range y ≠ 1
XY exchange x = 3Y / (3Y + 1) denominator and multiply it in the past
Let x denote y
The inverse function is y = x / (3-3x) x ≠ 1
How to find the inverse function of y = X-2 / 3x + 4
Y = (X-2) / (3x + 4), (x not = - 3 / 4)
Then: (3x + 4) y = X-2,
3xy+4y=x-2,
(3y-1)x=-4y-2,
So x = (4Y + 2) / (1-3y), (y not = 1 / 3)
Therefore, the inverse function is;
Y = (4x + 2) / (1-3x), (x not = 1 / 3)
The method of finding the inverse function of a function is to obtain x = g (y) by identity transformation of function y = f (x), and then exchange X and y, that is to say
The inverse function y = g (x) of function y = f (x), remember to write out the definition field
Y = 3x-2 (x > 2) inverse function
∵ y=3x-2 （x＞2）∴ y>4
From y = 3x-2 (x > 2), x = y + 2 / 3 is obtained
So the inverse function y = 3x-2 (x > 2) is y = x + 2 / 3 (x > 4)
The function y = x ^ 2-3x (x
y=x^2-3x
=(x-3/2)^2-9/4
Because x = - 2)
The inverse function y = 3x + 1 of X-2,
The solution consists of y = X-2 parts 3x + 1
Xy-2y = 3x + 1
That is, X (Y-3) = 2Y + 1
That is, x = (2Y + 1) / (Y-3)
So the inverse function is y = (2x + 1) / (x-3) (x ≠ 0)
The inverse function of y = (3x + 5) parts x (x ∈ R, and X ≠ - 5 / 3)
Let y = x / (3x + 5)
Then 3xy + 5Y = X
5y=x(1-3y)
x=5y/(1-3y)
Swap x with y
Y = 5x / (1-3x) (and X does not = 1 / 3)
Find the inverse function of y = x + 2x-1, and find the definition domain and value range of inverse function?
y=(3x-1)/(x+2)
xy+2y-3x+1=0
x(y-3)=-1-2y
x=(1+2y)/(3-y)
Y = (1 + 2x) / (3-x) the domain x is not equal to 3, and the range y is not equal to - 2
Where (x) is the base function of log (1) = (1) Let f (x) = log log the logarithm of (1 + X / 1-x) with a as the base (where a > 0 and a is not equal to 1) (1) find the definition domain (2) of the function
(1) ∵ 1 + x > 0 and 1-x > 0
ν x ∈ (- 1,1), and the definition domain of the function is (- 1,1);
Y = log the inverse function of the logarithm of x = B / X-B (a > 0, b > 0 and a is not equal to 1)
a^y=(x+b)/(x-b)
x*a^y-b*a^y=x+b
(a^y-1)x=b(a^y+1)
x=b(a^y+1)/(a^y-1)
So the inverse function y = B (a ^ x + 1) / (a ^ x-1)
Given that the image of the inverse function of the logarithm of the base X of y = log (a > 0 and a is not equal to 1) passes through the point (1,3), then a is equal to? My solution is: According to the meaning of the title, the inverse function of the logarithm of X with a as the base (a > 0 and a is not equal to 1) is: A ^ y = x; Put (1,3) into a ^ y = x, get a ^ 3 = 1, get a = 1, why is this not in the answer``` `
The inverse function is not: A ^ y = x;
We also need to exchange X and y, that is, a ^ x = y
Substitute (1,3) into a ^ x = y, 3 = a
RELATED INFORMATIONS
- 1. The function f (x) = log logarithm with a as base (2x-1), G (x) = log logarithm of log with a as base (x + 3), where a is greater than 0 and a is not equal to 1, when x is taken respectively: (1) f (x) = G (x) (2) f (x) is less than g (x)
- 2. If the inverse function of the function f (x) = x + A / BX + C is 3x + 1 / 2x-1, then what is the value of a, B, C and the symmetry center of F (x)? a. The value of B and C can be calculated, that is, the center of symmetry can not be calculated
- 3. The known function f (x) = a − x If the symmetry center of the inverse function image of X − a − 1 is (- 1,3), then the value of real number a is () A. 2 B. 3 C. -3 D. -4
- 4. If the image of the inverse function of the function f (x) = loga x passes through the point (- 1,2), then a = ()
- 5. Find the definition domain and value range of the inverse function f ^ (- 1) of the function f (x) = 2x-1 / x + 1
- 6. Let y = f (x), y = g (x) have inverse functions, and the function images of F (x-1) and g-1 (X-2) are symmetric with respect to the straight line y = X. if G (5) = 1999, then f (4)=______ .
- 7. Let f ^ - 1 (x) be the inverse function of the function f (x) = log2 ^ (x + 1). If (1 + f ^ - 1 (a)) is multiplied by (1 + f ^ - 1 (b) = 8, then the value of F (a + B) is obtained
- 8. Value range y = 5x-1 / 4x + 2! I have worked out the whole process. The main reason is why 7 / (8x + 4) ≠ 0?
- 9. Images and properties of reciprocal functions Senior one elective course,
- 10. Is a function with inverse function necessarily continuous
- 11. It is known that the function y = f (x) is an odd function. When x is greater than or equal to 0, f (x) = 3x + 1. If the inverse function of F (x) is y = g (x), then G (negative 8) =? Urgent
- 12. Inverse function of y = ln + 1 Come on, I'm in a hurry
- 13. Minus 3-2x is the square of 5x. The polynomial of 3x-8 is A. 5 (square of x-x) - 11 B. The square of 5x-x-11 C. The square of - 5x + X + 11 C. 5 (square of x-x-1)
- 14. The square of (x + 1) + the square of (2x + 1) is equal to the square of (3x + 2) (2x + 1)
- 15. Inverse function of y = 1-radical (1-x ^ 2) (- 1 less than or equal to x less than 0)
- 16. y=cosx（-pai/2
- 17. The known point P (1,2) is on the image of the function y = the following sign ax-b, and at the same time find a * B on its inverse function
- 18. If the inverse function of function f (x) is f ^ - 1 (x), and the image of y = f (x / 2) is symmetric to the image of y = e ^ X-1 with respect to y = X-1, then f ^ - 1 (1) =?
- 19. Let f (x) = (AX + 3) / (2-x), if f (x) is equal to its inverse function, find the real number a
- 20. Inverse function problems in senior one What is the inverse function of y = 10 to the x power + 10 to the negative x power divided by 10 to the x power - 10 to the negative x power?