Question

If f(x)=kx^3-1 and f^-1 (15)= 2, find k

Answer 1

k = 2

Explanation:

Okay, the first thing we need to do here is find the inverse of the equation given.

f(x) = kx^3 -1

Let f(x) = m

m = kx^3 -1

m + 1 = kx^3

(m+1)/k = x^3

x = 3x√(m+1)/k

Thus, the inverse is;

f^-1(x) = 3x√(x + 1)/k

now let’s make the substitution for f^-1(15)

2 = 3x√(15+1)/k

2 = 3x√(16/k

Cube both sides

2^3 = 16/k

8 = 16/k

8k = 16

k = 16/8 = 2