Answer:
The missing term is 20
Step-by-step explanation:
Given
[tex]f(x) = \frac{1}{2}x + 10[/tex]
[tex]h(x) = 2x -[/tex] --- inverse of f(x)
Required
Complete h(x)
We have:
[tex]f(x) = \frac{1}{2}x + 10[/tex]
Express f(x) as y
[tex]y = \frac{1}{2}x + 10[/tex]
Swap x and y
[tex]x = \frac{1}{2}y + 10[/tex]
Multiply through by 2
[tex]2x = y + 20[/tex]
Make y the subject
[tex]y = 2x - 20[/tex]
Replace y with the inverse function
[tex]h(x) = 2x - 20[/tex]
Compare
[tex]h(x) = 2x - 20[/tex]
with
[tex]h(x) = 2x -[/tex]
The missing term is 20
