Inverse of the give function F(x) = ( x + 4 )³ - 1 is F⁻¹(x) = [√( x + 1 ) ] - 4.
Given is a function of x, F(x) = ( x + 4 )³ - 1
These question can be solved by following 4 easy steps
Step 1 : Switch the F(x) with the variable y
This implies, F(x) = ( x + 4 )³ - 1 becomes y = ( x + 4 )³ - 1
Step 2 : Interchange the variable x and y in the above obtained equation
This implies, from the equation y = ( x + 4 )³ - 1, we get
x = ( y + 4 )³ - 1
Step 3 : Solve the new obtained equation for y
This implies, we have to simplify the equation by rearranging the terms to get the equation in terms of the variable x.
x = ( y + 4 )³ - 1
=> x + 1 = ( y + 4 )³
=> (y + 4 )³ = x + 1
=> y + 4 = √( x + 1 )
=> y = √( x + 1 ) - 4
Hence we obtain the required equation.
Step 4 : Switch the variable y with F⁻¹(x)
This implies, y = √( x + 1 ) - 4 becomes F⁻¹(x) = √( x + 1 ) - 4
Therefore, we get the inverse of the give function F(x) = ( x + 4 )³ - 1 as F⁻¹(x) = [√( x + 1 ) ] - 4.
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