Answer:
[tex]\huge\boxed{h(x) = \frac{1}{2} x - \frac{1}{2}}[/tex]
Step-by-step explanation:
[tex]f(x) = 2x+1[/tex]
Put f(x) = y
[tex]y = 2x + 1[/tex]
Interchange x and y
[tex]x = 2y+1[/tex]
Solve for y
[tex]x = 2y+1[/tex]
Subtracting 1 to both sides
[tex]x-1 = 2y[/tex]
Dividing both sides by 2
[tex]\frac{x-1}{2} = y \\\\ OR\\\\ y = \frac{x-1}{2}[/tex]
Put y = h(x)
[tex]\bold{h(x) = \frac{1}{2} x - \frac{1}{2}}[/tex]
