Question

The one-to-one functions g and h are defined as follows.

g(x) =
x+13
5
h={(-4, -7), (-1, 5), (0, 3), (8, -4)}
Find the following.
g'(x) = 0
9
h ¹(-4) =
I need help please

Answer 1

Explanation:

again, I assume the -1 exponent means "inverse function" and not 1/function.

the inverse function of g(x) :

g(x) = y = (x + 13)/5

5y = x + 13

5y - 13 = x

now we rename y to x and vice versa, so that we create a "normal" function :

g-¹(x) = y = 5x - 13

(g-¹ × g)(2) = (5×2 - 13)×(2 + 13)/5 =

= (10 - 13)×15/5 = -3×3 = -9

h-¹(4) means the x-value when h(x) = 4.

but there is no h(x) = 4.

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