The inverse function will be x = [tex]f^{-1}[/tex](y) = 4 + [tex]\frac{a}{y-2}[/tex]
Step-by-step explanation:
Given,
y = [tex]\frac{a}{x-4} + 2[/tex]
To find the inverse of this function means we have to find the value of x in terms of y
Now,
y = [tex]\frac{a}{x-4} +2[/tex]
or, y - 2 = [tex]\frac{a}{x-4}[/tex] [ subtracting 2 from both side]
or, (y-2)(x-4) = a [ by cross multiplication)
or, x-4 = [tex]\frac{a}{y-2}[/tex]
or, x = 4 + [tex]\frac{a}{y-2}[/tex]
Hence, x = [tex]f^{-1}[/tex](y) = 4 + [tex]\frac{a}{y-2}[/tex]
