Some problems about inverse function in senior one 1. Simplification: arcsin (SIN3)= 2. Function y = arccos (SiNx) (- Pai / 3

Some problems about inverse function in senior one 1. Simplification: arcsin (SIN3)= 2. Function y = arccos (SiNx) (- Pai / 3

1. Let arcsin (SIN3) = X
Then SiNx = xin3
The value range of X is [- pi / 2, PI / 2]
Then x = (PI-3)
2. First - pi / 3

1. Y = - x square + 6x-5 (| x | less than or equal to 2) 2. Y = root 2X-4 (x ≥ 4) One is a quadratic function, the other is a root sign, both are quadratic

One
y=-(x-3)^2+4
-2≤x≤2
-21≤y≤3
x=3±√(4-y)
x=3-√(4-y)
The inverse function
y=3-√(4-x)
-21≤x≤3
Two
x≥4
y≥2
x=(y^2+4)/2
The inverse function
y=(x^2+4)/2
x≥2

The main process of inverse function How to define the inverse function of function y = 10 ^ X-1

The original function range is the definition domain of inverse function
∵10^x＞0
∴y=10^x-1＞-1
The definition domain of its inverse function is (- 1, + ∞)

To find the inverse function of y = 3x-5 / 2x + 1, it is better to write the detailed process

y(2x+1)=3x-5
2xy+y=3x-5
3x-2xy=y+5
x=(y+5)/(3-2y)
So the inverse function y = (x + 5) / (3-2x), X ≠ 3 / 2

The known function f (x) = ax + 1 If the inverse function of X − 3 is f (x) itself, then the value of a is () A. -3 B. 1 C. 3 D. -1

X = ay + 1
y−3⇒y＝3x+1
x−a⇒f−1(x)＝3x+1
x−a⇒a＝3，
Therefore, C

How to find the inverse function of function f (x) = (1 + x) / ax

y=(1+x)/ax
axy=1+x
x=1/(ay-1)
So the inverse function is y = 1 / (AX-1)

The inverse function of the urgent function f (x) = ax ^ 2 + AX = 1 must cross the point_____ ?

Let's look at the point where the original function must pass, and then find the point where y = x is symmetric

If the inverse function of the function f (x) = (AX-2) / (x-1) (x ≠ 1) is f ^ (- 1) (x) = (X-2) / (x + 3), then a=

y=(ax-2)/(x-1)
Inverse solution
xy-y=ax-2
(y-a)x=y-2
x=(y-2)/(y-a)
The inverse function is obtained by exchanging variables
y=(x-2)/(x-a)
Because x-a = x + 3
So a = - 3

If the point (2,1 / 4) is on both the image of F (x) = 2 ^ ax + B and the image of its inverse function, find the value of A.B

(2,1 / 4) on the image with F (x) = 2 ^ ax + B, there is an equation
1/4=2^a*2+b.(1)
(2,1 / 4) on the image of the inverse function f (x) = 2 ^ ax + B, there is an equation
2=2^a*(1/4)+b.(2)
The simultaneous equations of (1) and (2) can be obtained
a. Please calculate the specific results

Point (1,2) on the image of function f (x) = radical ax + B, and on the image of its inverse function F-1 (x), find the values of a and B

From the meaning of the question, we know that points (1,2) and (2,1) are points on function f (x)
Then there is a + B = 4
2a+b=1
A = - 3. B = 7