Question

find the domain and simplified formula for the inverse f⁻1 of the following function f(x)= √(5x-2)

find the domain and simplified formula for the inverse f⁻1 of the following function f(x)= 2x^3+8

please and thanks:)

Answer 1

1. f-1 = (x^2 +2)/5
2. f-1 = [(x-8)/(2)]^(1/3)

Answer 2

second one

\[f(x)=2x^3+8\] has domain all real numbers. range as well
function says
1) cube
2) double
3) add 8

inverse will say
1) subtract 8
2) divide by 2
3) take the cube root. get
\[f^{-1}(x)=\sqrt[3]{\frac{x-8}{2}}\]

Answer 3

central science and u please show me how you got the answer im trying to figure it cause i need to learn it for my college algebra class please and thanks if you dont mind

Answer 4

To find inverse functions, you must first check if the original function is one-to-one, meaning that if you draw the graph of that function, it passes the Horizontal Line Test. The Horizontal Line Test states that a function is one-to-one if any horizontal line intersects that function at at most 1 point.
If a function does have an inverse, you can find it by interchanging x and y and solving.

For example, y = 2x +1 would become x = 2y + 1. You would then solve for this new y.

Answer 5

oh ok yes that makes sense i remember some of that from class