Hey there :)
f ( x ) is also y
So [tex]f(x)= \frac{2x+7}{x+1} [/tex] is [tex] y = \frac{2x+7}{x+1} [/tex]
To find the inverse, reverse the places of x and y, let y be in the place of x and x in the place of y
↓
[tex]x = \frac{2y+7}{y+1} [/tex]
x ( y + 1 ) = 2y +7
xy + x = 2y + 7
xy - 2y = 7 - x
Take y as common factor
y ( x - 2 ) = 7 - x
Divide by x - 2 on either side to isolate y and thus find the inverse
[tex] \frac{y(x-2)}{(x-2)} = \frac{7-x}{x-2} [/tex]
y = [tex] \frac{7-x}{x-2} [/tex]
Therefore the inverse of the function is:
f ⁻¹ ( x ) = [tex] \frac{7-x}{x-2} [/tex]
