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The inverse function of f(x) = 1/2x + 1/4 is f-1(x) = 2x - 1/2
The function is given as:
f(x) = 1/2x + 1/4
Rewrite the function as
y = 1/2x + 1/4
Swap the positions of x and y
x = 1/2y + 1/4
Multiply through by 4
4x = 2y + 1
Subtract 1 from both sides
2y = 4x - 1
Divide by 2
y = 2x - 1/2
Rewrite as an inverse function
f-1(x) = 2x - 1/2
Hence, the inverse function of f(x) = 1/2x + 1/4 is f-1(x) = 2x - 1/2
See attachment for the graph of the inverse function
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