Inverse of the give function F(x) = √2 x + 1 is F⁻¹(x) = ( x - 1 ) / √2
Given is a function of x, F(x) = √2 x + 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) = √2 x + 1 becomes y = √2 x + 1
Step 2 : Interchange the variable x and y in the above obtained equation
This implies, from the equation y = √2 x + 1, we get
x = √2 y + 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 = √2 y + 1
=> x - 1 = √2 y
=> √2 y = x - 1
=> y = ( x - 1 ) / √2
Hence we obtain the required equation.
Step 4 : Switch the variable y with F⁻¹(x)
This implies, y = ( x - 1 ) / √2 becomes F⁻¹(x) = ( x - 1 ) / √2
Therefore, we get the inverse of the give function F(x) = √2 x + 1 as F⁻¹(x) = ( x - 1 ) / √2.
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