Question

Given that f(x) = x/3 - 1 and that g(x)=2x-5 a) Work out f(6) + g(3) b) Work out g^-1(7) c) Work out g^-1(7) – f^-1(1)​

Answer 1

A) 2 B) 6 C)0

Explanation:

A)

f(6) = 6/3 - 1 = 1

g(3) = 2(3) - 5 = 1

f(6) + g(3) = 1 + 1 = 2

B)

Find the inverse of the function g(x)

x = 2y-5

-2y = -x-5

2y = x+5

y = (x+5)/2

g^-1(7) = 12/2 = 6

C)

g^-1(7) = 6

Find the inverse of the function f(x)

x = y/3 - 1

x+1 = y/3

y = 3x+3

f^-1(1) = 3+3 = 6

g^-1(7) – f^-1(1)​ = 6-6 = 0