簡易數學function題

A
h(x) = 4x - 9

(a) Find h⁻¹ (x) (the inverse of h(x)).

Let y = h(x) = 4x - 9
y + 9 = 4x
x = (y + 9)/4
y = h(x)
x = h⁻¹ (y) = (y + 9)/4
h⁻¹ (x) = (x + 9)/4


(b) Find the value of (h⁻¹ 。h) (3).

(h⁻¹ 。h) (3)
= h⁻¹( h(3) )
= h⁻¹( 4×3 - 9 )
= h⁻¹( 3 )
= (3 + 9)/4
= 12/4
= 3

Remark:
Actually, (h⁻¹ 。h) (x) = h⁻¹( h(x) ) = x for sure.


B
g = { (-1, 4), (4, 8)}

means g(-1) = 4 and g(4) = 8

Thus, g⁻¹ (4) = -1