# What is the inverse function of #f(x) =5x^3 + 4x^2 + 3x + 4#?

The simplest way to write the inverse function is to write

#x=5y^3+4y^2+3y+4#

This can be written explicitly (in terms of

#x=-(15 sqrt(3) sqrt(675 y^2-4576 y+7900)-675 y+2288)^(1/3)/(15 (2^(1/3)))+(29 (2^(1/3)))/(15 (15 sqrt(3) sqrt(675 y^2-4576 y+7900)-675 y+2288)^(1/3))-4/15#

Graph:

By signing up, you agree to our Terms of Service and Privacy Policy

To find the inverse function of ( f(x) = 5x^3 + 4x^2 + 3x + 4 ), we can follow these steps:

- Replace ( f(x) ) with ( y ).
- Swap ( x ) and ( y ) to switch the roles of the independent and dependent variables.
- Solve the resulting equation for ( y ).
- Replace ( y ) with ( f^{-1}(x) ) to express the inverse function.

Following these steps, we have:

[ x = 5y^3 + 4y^2 + 3y + 4 ]

Now, we solve this equation for ( y ).

[ 0 = 5y^3 + 4y^2 + 3y + 4 - x ]

Unfortunately, there's no general method for finding the inverse of a cubic function like ( f(x) = 5x^3 + 4x^2 + 3x + 4 ). While certain functions have inverses that can be expressed with elementary functions, cubics often do not have such inverses that can be represented using basic arithmetic operations and elementary functions. Therefore, unless there are specific instructions or conditions provided that might make it possible to find the inverse using particular techniques, we generally leave the function as it is, without finding its inverse.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you find the Vertical, Horizontal, and Oblique Asymptote given #x/(x^2+x-6)#?
- How do you find the vertical, horizontal and slant asymptotes of: #y = (2 + x^4)/(x^2 − x^4) #?
- How do I identify the horizontal asymptote of #f(x) = (7x+1)/(2x-9)#?
- Given the functions #F(x)=x+4# and #G(x)=2x^2+4# what is f(g(x))?
- How do you use the horizontal line test to determine whether the function #f(x)=1/8(x+2)^2-1# is one to one?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7