Question

Assume the function has an inverse. Without solving for the inverse find the indicated function values: f(x)=x^3+4x-1, (a) f^-1 (-1) (b) f^-1 (4) ...?

Answer 1

To find the indicated function values of the inverse of a function, substitute the given values into the original function and solve for x.

Step-by-step explanation:

To find the indicated function values of the inverse of the function f(x)=x^3+4x-1, without solving for the inverse function, we substitute the given values into the original function and solve for x.

(a) To find f^-1(-1), we substitute -1 into the function: f(-1)=(-1)^3+4(-1)-1 = -1+(-4)-1 = -6.

(b) To find f^-1(4), we substitute 4 into the function: f(4)=(4)^3+4(4)-1 = 64+16-1 = 79.

Answer 2

f(x) = x³ + 4x - 1

The domain of a function is the range of its inverse and the range of a function is the domain of its inverse. Thus, to find f⁻¹(x), we put the given value of x into f(x) of the original equation.

a) -1 = x³ + 4x - 1
x = 0
f⁻¹(-1) = 0

b) 4 = x³ + 4x - 1
x = 0.25
f⁻¹(4) = 0.25