Find the Inverse
What is the inverse of
j(x)=(2x+3)/4
What is
j^-1(x)=2x-3/2
f(x)=(x-5)/10
h(x)=10x+5
What is Yes
The inverse notation for the function
f(x)
What is
f^-1(x)
f(x) is a function with the following steps:
1. Multiply by 2
2. Square the quantity
3. Add 9
f(x)=(2x)^2+9
What is the inverse of
f(x)=3x+1
What is
f^-1(x)=(x-1)/3
f(x)=3(x-9)
g(x)=1/3x+9
What is Yes
The graph of a function that passes through the point (-3,4). What point must lie on the graph of the function's inverse?
What is (4,-3)
If f(x) is a function with the following steps:
1. Add 3
2. Multiply by 5
which steps would occur in f ^-1(x)?
First divide by 5 and then subtract 3
The inverse of
g(x)=(8-5x)/4
What is
g^-1(x)=(4x-8)/5
f(x)=x+10
g(x)=-x-10
No
True or false: a function and its inverse can never intersect
What is false
Example:
f(x)=2x, f^-1(x)=x/2
If f(x) is a function with the following steps:
1. Add 3
2. Multiply by 5
How would we write the inverse function, f ^-1(x)?
f^−1(x)=x/5−3
What is the inverse of
g(x)=1/2(x-6)
What is
g^-1(x)=2x+6
g(x)=(8+9x)/2
f(x)=(5x-9)/2
What is No
When given the domain and range of a function but not the actual function, what information do I know about the inverse function?
What is the domain and range of my inverse function by interchanging x & y
What is the inverse of the given coordinates: (1, 2) (3, 8) (-3, 6)
(2, 1) (8, 3) (6, -3)
What is the inverse of
f(x)=x^2+4
What is
f^-1(x)=+-sqrt(x-4)
f(x)=2x+2
g(x)=2x-2
No
True or false: a function can be its own inverse
What is true
Examples:
y=x, y=-x+3
When finding the inverse of a relation,
1st you replace f(x) with y
2nd switch the x's and y's
What do you do next?
Solve for y in terms of x . y = f^-1(x)