Answer:
[tex]h(x) = \frac{1}{2} x+ 5[/tex]
Step-by-step explanation:
To find the inverse of a function, simply switch the 'x' and 'y' variables. Substitute in 'y' in the place of f(x) for this purpose:
y = 2x - 10
Switch positions:
x = 2y - 10
Add '10' to both sides to begin simplifying:
x + 10 = 2y
Divide both sides by 2:
[tex]y= \frac{x+10}{2}[/tex]
This can be rewritten as:
[tex]y = \frac{1}{2} x+ 5[/tex]
Therefore, the inverse of the function is:
[tex]h(x) = \frac{1}{2} x+ 5[/tex]
