Question

Plzzz help asapppppp what is the inverse of f if f(x)=^3 sqrt x-5

Answer 1

If you want it short and simple:

f^-1 = x^3 + 5

If you wanna stay for the ride:

f(x) is basically a fancy way of saying y. So we are solving for the inverse of

y = ^3 sqrt x - 5 (the cube root of x - 5). When solving an inverse, just simply swap the x's and y's!. This'll make x = ^3 sqrt y - 5, or the cube root of y - 5.

Now that all that is over with, we solve:

Remember, our new equation is

x = ^3 sqrt y - 5

To get rid of the annoying radical, cube both sides, or add a power of 3 to both sides.

x^3 = y - 5

Squaring a square root or cubing a cube root will always get

rid of the radical.

Now it's just the basic stuff:

+ 5 x^3 = y - 5 + 5                (add 5 to both sides)

Don't forget to change "y" to f^-1!

Your answer is f^-1 = x^3 + 5, or option A.

NOTE: f^-1 is fancy for the inverse. It basically means the same thing as "y". y = x^3 + 5 means the same thing.

An easy step-by-step list of what to do in inverse problems:

1. Switch f(x) to y (this just helps keep things lookin' simple)

2. swap x and y values (ex: y=2x would become x=2y)

3. SOLVE! (use your algebra tools)

If there is any confusion then please comment! I'd love to help!

                     

Answer 2

Hello from MrBillDoesMath!

Answer:

The first choice, y = x^3 + 5

Discussion:

Let

y = (x-5) ^ (1/3)

To find the inverse, sway x and y and then solve for y:

x = ( y - 5 )^(1/3)         =>             cube both sides

x^3 = y - 5                  =>             add 5 to both sides

x^3 + 5 = y

So the inverse is  x^3 + 5, which is the first choice

Thank you,

MrB