Calc I HW help please

[Techie333]

Can somebody help me. How would I get the inverse of this fuction:

f(x) = (x^2) + (sqrt (x)) + 2?

I know you replace the x's with the y's and solve for y but then I get:

x = (y^2) + (sqrt (y)) + 2 and I don't know how to factor that?

 

[chuckywang]

That function has no roots, so it'll be really really hard to factor.

 

[txrandom]

Are you sure you are suppose to factor it? Can you just leave it how you have it?

 

[Techie333]

Well the problem says to find the range of the inverse and compute it at f^-1(4)

The range is: x>0 and i think it is = 1 @ 4? How do u find it at 4?

 

[SpecialEd]

you don't need the inverse function explictly to find the range of the inverse function. Clearly the domain of f is [0,infty) and the range is [2, infty). Thus the inverse function will have domain [2, infty) and range [0, infty).

To find f^-1 (14), solve the equation 14=x^2+sqrt(x)+2

 

[Techie333]

Originally posted by: SpecialEd
you don't need the inverse function explictly to find the range of the inverse function. Clearly the domain of f is [0,infty) and the range is [2, infty). Thus the inverse function will have domain [2, infty) and range [0, infty).

To find f^-1 (14), solve the equation 14=x^2+sqrt(x)+2

Sorry, but how do u do that?

 

[chuckywang]

Originally posted by: Techie333
Well the problem says to find the range of the inverse and compute it at f^-1(4)

The range is: x>0 and i think it is = 1 @ 4? How do u find it at 4?

The range of the inverse is just the domain of the function. Obviously, the domain is x>=0 with the square root in that function.

Also note that f(1) = 4, so f^(-1) (4) = 1.

 

[SpecialEd]

Originally posted by: Techie333

Originally posted by: SpecialEd
you don't need the inverse function explictly to find the range of the inverse function. Clearly the domain of f is [0,infty) and the range is [2, infty). Thus the inverse function will have domain [2, infty) and range [0, infty).

To find f^-1 (14), solve the equation 14=x^2+sqrt(x)+2

Sorry, but how do u do that?

I see you want f^-1 (4)

so f(1)=1+1+2=4. Thus by the definition of inverse function, f^-1 (4)=1. The answer of 1 is an educated guess. But you can show it's true just by looking at f.

 

[Techie333]

Yes of course! Thank you, my friends!

 

[Estrella]

that is more of a cal 2 question

I can explain it but, it is not normally cal I material.