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 (4)

Answer 1

you can use definition of inverse

if (x,y) is in f , then (y,x) is in f^-1

Answer 2

I've a problem with factorizing x^3+4x-5=0

Answer 3

no need to factor

Answer 4

we have by definition
f^-1 (y)=x <=> f(x) = y

Therefore in our example
f^-1 (4) = x <=> f(x) = 4

now solve f(x) = 4

Answer 5

f(x) = 4

x^3+4x-1 = 4

x^3 + 4x - 5 = 0

(easy solution x = 1 )

so

f(1) = 4

so f^-1 (4) = 1

Answer 6

My problem is from where did the x=1 came from! i need a way to factorize x^3 + 4x - 5 = 0 to give me x=1 other than trying numbers that satisfy the equation mentally