1.) Find (f + g)(x) when f(x) = x + 2 and g(x) = x - 2.
2.) Find (f - g)(x) if f(x) = 2x - 5 and g(x) = 4.
3.) Given f(x) = 4 and g(x) = 2x - 1, find (f - g)(x).
(f+g)(x) = x + x + 2 - 2 = 2 x
do the others the same way
To find (f + g)(x), we need to add the functions f(x) and g(x).
1.) Find (f + g)(x) when f(x) = x + 2 and g(x) = x - 2:
Start by substituting the given functions into the equation for (f + g)(x):
(f + g)(x) = f(x) + g(x)
Now substitute the functions:
(f + g)(x) = (x + 2) + (x - 2)
Next, simplify the expression:
(f + g)(x) = x + 2 + x - 2
Combining like terms:
(f + g)(x) = 2x
So, (f + g)(x) = 2x.
2.) Find (f - g)(x) if f(x) = 2x - 5 and g(x) = 4:
To find (f - g)(x), we need to subtract the function g(x) from f(x).
Start by substituting the given functions into the equation for (f - g)(x):
(f - g)(x) = f(x) - g(x)
Now substitute the functions:
(f - g)(x) = (2x - 5) - 4
Next, simplify the expression:
(f - g)(x) = 2x - 5 - 4
Combining like terms:
(f - g)(x) = 2x - 9
So, (f - g)(x) = 2x - 9.
3.) Given f(x) = 4 and g(x) = 2x - 1, find (f - g)(x):
To find (f - g)(x), we need to subtract the function g(x) from f(x).
Start by substituting the given functions into the equation for (f - g)(x):
(f - g)(x) = f(x) - g(x)
Now substitute the functions:
(f - g)(x) = 4 - (2x - 1)
Next, simplify the expression:
(f - g)(x) = 4 - 2x + 1
Combining like terms:
(f - g)(x) = -2x + 5
So, (f - g)(x) = -2x + 5.