Question

Which function is the inverse of f(x) = 4x^3 - 2?

Answer 1

Answer:

$g(x)=\sqrt[3]{\frac{x+2}{4}}$

Step-by-step explanation:

$y=4x^3-2$

$x=4y^3-2$

$4y^3-2=x$

$4y^3-2+2=x+2$

$4y^3=x+2$

$\frac{4y^3}{4}=\frac{x}{4}+\frac{2}{4}$

$y^3=\frac{x+2}{4}$

$y=\sqrt[3]{\frac{x+2}{4}}$

$g(x)=\sqrt[3]{\frac{x+2}{4}}$

Answer 2

The inverse function of f(x) = 4x² - 2 will be g(x) = ∛(x+4)/2.

What is an inverse function?

The function in which the value of variables is interchanged is called an inverse function. In other words, the inverse function is one in which the value of x is replaced by y and vice versa.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The inverse function will be calculated as below:-

y = 4x³ - 2

x = 4y³ - 2

4y³ - 2 = x

4y³ - 2 + 2 = x + 2

4y³ = x + 2

y³ = (x/4) + (2/ 4)

y³ = ( x+2 ) / 4

y =  ∛(x+4)/2.

Therefore, the inverse function of f(x) = 4x² - 2 will be g(x) = ∛(x+4)/2.

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