if possible fin a) f^-1 (5) b) g^-1 (6)

Question

Needing some help with this problem

Answer 1

(a) for example, if f(x) = 2x-1, then f^-1(x) =(x+1)/2,

f^-1(5)= (5+1)/2 = 6/2= 3

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

y=2x-1 becomes x=2y-1

2y =x+1

y = (x+1)/2= f^-1(x)= the inverse function which is a reflection over the diagonal line y=x

(b) let g(x) = x^2 + 3, then switch x and y to get x = y^2 +3, solve for the new y

y^2 =x-3, y= +/-sqr(x-3)= g^-1(x)

g^-1(6) = +/-sqr(6-3) = +/-sqr3 = about +/-1.732

or whatever h^-1(x) its inverse = h(x) and vice versa