Find f^-1 for the function f(x)=(x-10)^3+4

f^(-1)(x)=(x-4)^(1/3)+10

Step-by-step explanation:

So to find the inverse we need to first solve the equation y=(x-10)^3+4 for x.

Subtract 4 on both sides:

y-4=(x-10)^3

Cube root (or raise both sides to 1/3 power):

(y-4)^(1/3)=x-10

Add x on both sides:

(y-4)^(1/3)+10=x

Swap x and y:

(x-4)^(1/3)+10=y

Symmetric property of equality:

y=(x-4)^(1/3)+10

So f^(-1)(x)=(x-4)^(1/3)+10.

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step-by-step explanation:

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204