Answer:
[tex]f(x + h) - f(x) = h^2 + 3h - 5[/tex]
Step-by-step explanation:
Given
[tex]f(x) = x^2 + 3x - 5[/tex]
Required
Find f(x + h) - f(x)
In functions:
[tex]f(x + h) = f(x) + f(h)[/tex]
So:
[tex]f(x + h) - f(x) = f(x) + f(h) - f(x)[/tex]
Collect Like Terms
[tex]f(x + h) - f(x) = f(x) - f(x)+ f(h)[/tex]
[tex]f(x + h) - f(x) = f(h)[/tex]
Solving for f(h)
[tex]f(h) = h^2 + 3h - 5[/tex]
So:
[tex]f(x + h) - f(x) = h^2 + 3h - 5[/tex]
