assume that f is one-to-one function

Question

(a) If f(4) = 3, find f⁻¹(3).

(b) If f⁻¹(6) = −7, find f(−7).

Answer 1

a) 4

b) 6

just think in reverse, for the inverse

time travel to the past

the inverse function takes you back to where you started

f(4)=3

f^-1(3) =4

f(f^-1(x)) = x

f^-1(f(x) = x

f(f^-1(3))=f(4)=3

f(4)=3 is the graphically the point (4,3)

switch the x and y coordiates for the inverse, (3,4)

g(3)=4 is the inverse funciton, f^-1(3)=4

f^-1(6) =- 7 is the point (6,-7)

switch x and y values to get the inverse point, (-7,6)

f(x)=y

f(-7)=6