1. Let f(x) = sqrt x + 3, what is the equation for f^-1 (x).
2. If f(x) = x+3/4, what is the equation for f^-1(x)
3. If f(x) = x^2 + 7, what is the equation for f^-1(x)
4.If f(x) = sqrt 3x + 2, what is the equation for f^-1(x)
HELP PLEASE THANKS!
In general, finding the inverse of a function consists of two main steps:
1. After writing the original function in the form y = ...., interchange the x and y variables
2. solve this new equation for y
I will do one of them, you do the others:
f(x) = √(x+3) ----> y = √(x+3)
interchange: ----> x = √(y+3)
square both sides
x^2 = y + 3
y = x^2 - 3
This one is a bit tricky: The domain of the original becomes the range of its inverse, and the range of the original becomes the domain of its inverse.
so the domain of the original was x ≥ -3, then the range of
y = x^2 - 3 must be y ≥ -3 , thus x^2 - 3 ≥ -3 and x^2 ≥ 0, and x ≥ 0
so f^-1(x) = x^2 - 3 , x ≥ 0
You will need the same discussion in #4.
#2 is easy
let me know what you got for #3
remember that the graph of your inverse equation should be a reflection in the line y = x
Another way to check to check your answer:
Make a table of values of x and y for the original function
Make a new table of values by reversing the x's and y's
Plot this new set of points, it should be a reflection in the line y=x
Sure! I'll be happy to help you find the equations for the inverses of these functions. To find the inverse of a function, we need to switch the roles of x and y and then solve for y.
1. Let f(x) = sqrt(x) + 3. To find f^(-1)(x), we switch x and y: x = sqrt(y) + 3. Now let's solve for y.
x - 3 = sqrt(y)
(x - 3)^2 = y
Therefore, the equation for f^(-1)(x) is y = (x - 3)^2.
2. Let f(x) = (x + 3)/4. To find f^(-1)(x), we switch x and y: x = (y + 3)/4. Now let's solve for y.
4x = y + 3
y = 4x - 3
Therefore, the equation for f^(-1)(x) is y = 4x - 3.
3. Let f(x) = x^2 + 7. To find f^(-1)(x), we switch x and y: x = y^2 + 7. Now let's solve for y.
x - 7 = y^2
y = sqrt(x - 7)
Therefore, the equation for f^(-1)(x) is y = sqrt(x - 7).
4. Let f(x) = sqrt(3x) + 2. To find f^(-1)(x), we switch x and y: x = sqrt(3y) + 2. Now let's solve for y.
x - 2 = sqrt(3y)
(x - 2)^2 = 3y
y = (x - 2)^2/3
Therefore, the equation for f^(-1)(x) is y = (x - 2)^2/3.
I hope this helps! Let me know if you have any further questions.