Question

A function of g is g(x) = mx + c. Given that g⁻¹(-3) = 0 and g⁻¹(1) = 2, find the value of g(5) and g⁻¹(4)

Answer 1

Step-by-step explanation:

$y = mx + c \\ \\ mx = y - c \\ \\ x = \frac{y - c}{m} \\ \\ therefore \: \: \: \: {g}^{ - 1} = \frac{x- c}{m} \\ \\ {g}^{ - 1} ( - 3) = 0 \\ \\ \frac{ - 3 - c}{m} = 0 \\ \\ c = - 3 \\ \\ {g}^{ - 1} (1) = 2 \\ \\ \frac{1 - c}{m} = 2 \\ \\ 1 + 3 = m \\ \\ m = 4 \\ \\ g(x) = mx + c \\ \\ g(5) = 5m + c \\ \\ = 5(4) - 3 \\ \\ = 17. \\ \\ {g}^{ - 1} (4) = \frac{4 - c}{m } \\ \\ = \frac{4 + 3}{4} \\ \\ = \frac{7}{4} .$