f⁻¹(x) = ¹/₂ x - ³/₂
Option 1
[tex]\boxed{ \ f(x) = 2x + 3} \rightarrow f^{-1}(x)? \ } [/tex]
Let [tex]\boxed{y = 2x + 3}[/tex]
Rewrite and set the function with subject x.
Both sides are subtracted by 3.
y - 3 = 2x + 3 - 3
y - 3 = 2x
2x = y - 3
Both sides are divided by 2.
[tex]\boxed{x = \frac{1}{2}y - \frac{3}{2}}[/tex]
Let's replace [tex]\boxed{x \ with \ f^{-1}(x)}[/tex] and [tex]\boxed{y \ with \ x}[/tex].
Thus, the inverse of f(x) = 2x + 3 is [tex]\boxed{\boxed{ \ f^{-1}(x) = \frac{1}{2}x - \frac{3}{2} \ }}[/tex]
Option 2
[tex]\boxed{ \ f(x) = 2x + 3} \rightarrow x = 2f^{-1}(x) + 3 \ } [/tex]
[tex]\boxed{ \ x - 3 = 2f^{-1}(x) \ }[/tex]
[tex]\boxed{ \ 2f^{-1}(x) = x - 3\ }[/tex]
[tex]\boxed{\boxed{ \ f^{-1}(x) = \frac{1}{2}x - \frac{3}{2} \ }}[/tex]
Note:
Keywords: the inverse of function, f(x) = 2x + 3, one-to-one, onto, domain, range, interchange
