Question

Type the correct answer in each box. Spell all words correctly, and use numerals instead of words for numbers.if necessary,use/for fraction bar(s) The function below has an input,x, and produces a specific output,c, f(x)=4x^3=c solve for and complete the equation and statements below. x=[ ]

Answer 1

To find the value of 'x' for the equation f(x) = 4x^3 = c, one must take the cube root of 'c' divided by 4. This algebraic process does not involve units, and the result will give the value of 'x'.

Step-by-step explanation:

To solve for x in the equation f(x) = 4x^3 = c, we need to express x explicitly in terms of c. This involves taking the cube root of both sides of the equation. The cube root of a number is the value that, when cubed, gives the original number. Therefore, x is the cube root of c divided by 4.

The equation to solve is:

x = ∛(c/4)

Where ∛ denotes the cube root.

This equation does not require unit conversion as it is algebraic and does not involve physical quantities with units. To obtain the value of x, we substitute the given value of c and calculate the cube root.

Answer 2

To produce "c" as output, x must be=\sqrt[3]{\frac{c}{4} }

Step-by-step explanation:

You are asked to find what "x" value renders "c" as answer when applied to the given function.

So we need to basically solve for "x" in the equation:
`4x^3=c`, that is isolate "x" on one side of the equal sign.

We do such by first dividing both sides of the equation by "4" so we isolate the cubic root that contains "x". Then, we apply the cubic root on both sides:

`4x^3=c\\x^3=(c)/(4) \\x=\sqrt[3]{(c)/(4) }`