Question

Find the inverse of the function f(x) = 3x³ - 7 A. f⁻¹ (x) = ³√x-7/3 B. f⁻¹ (x) = x+7/3 C. f⁻¹ (x) = 1/3x³-7 D. f⁻¹ (x) = ³√x+7/3

Answer 1

The inverse of the function f(x) = 3x³ - 7 is f⁻¹(x) = ³√(x+7)/3.

Step-by-step explanation:

To find the inverse of the function f(x) = 3x³ - 7, we need to interchange x and y and solve for y. So, let's start by replacing f(x) with y:

y = 3x³ - 7

Now, interchange x and y:

x = 3y³ - 7

Next, solve for y:

3y³ = x + 7

y³ = (x + 7) / 3

y = ³∛(x + 7) / 3

Therefore, the inverse of the function f(x) = 3x³ - 7 is f⁻¹(x) = ³∛(x + 7) / 3

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