Answer:
[tex]\frac{4x^2-1}{2}[/tex]
Step-by-step explanation:
To find the inverse set f(x) = x and replace every x term on the right to a y. Then solve for y.
[tex]f(x) = \frac{1}{2}[/tex] × [tex]\sqrt{2x+1}[/tex]
[tex]x=\frac{1}{2} (2y+1)^\frac{1}{2}[/tex] - Re-write the square root using power.
[tex]2x=(2y+1)^\frac{1}{2}[/tex] - Multiply by 2
[tex](2x)^2 =2y+1[/tex] - Square both sides to get rid of the square root.
[tex]4x^2 - 1 = 2y[/tex] - Multiply out the bracket and take one from both sides.
[tex]\frac{4x^2-1}{2} = y[/tex]
Now set y as the inverse of f(x).
