Let f(x)=x+4/x+8 f^−1(−3)=

Question

Let

Answer 1

If f(a) = b, then f^-1 (b) = a

To find f^-1(-3), solve the equation f(x) = -3 for x.

(x+4)/(x+8) = -3

x+4 = -3x - 24

4x = -28

x = -7

So, since f(-7) = -3, f^-1(-3) = -7

Answer 2

f^-1(-3) = -7

f(x) = y = (x+4)/(x+8)

to find the inverse, f(x)^-1, switch x and y and solve for y

x= (y+4)/(y+8)

xy + 8x =y+4

xy-y = 4-8x

y(x-1) = 4-8x

y = (4-8x)/(x-1) = f^-1(x)

f^-1(-3) = (4-8(-3))/(-3-1) = 28/-4 = -7