Solutions

Problem Set 8

Functions

For each function and inverse value below, determine if that value shown is correct or not:

a) f(x) = 2x+3 f^-1(9) = 3 Yes, since f(3) = 2*3 + 3 = 9

b) f(x) = x³+3 f^-1(30) = 3 Yes since f(3) = 3³ + 3 = 30

c) f(x) = 8/x + 5 f^-1(9) = 3 No since f(3) = 8/3 + 5 which is not 9.

d) f(x) = log₁₀(x) f^-1(-2) = .01 Yes the log₁₀ of .01 is -2 because 10^-2 = .01

e) f(x) = log₁₀(x) f^-1(1000) = 2 No. The log₁₀ (2) is much less than 1000 (or even 1!)