Question

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!

Answer 1

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