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

k = 2

Step-by-step 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

y = i/2 xtnop + (3i/2 tnop+ 1)

step-by-step explanation:

the picture is the step by step explanation.

for this case we have that by definition, the volume of a cylinder is given by:

where:

r: it's the radio

h: it's the height

we have as data that:

substituting:

so, the cylinder volume is

option d