The functions of f(x), g(x), and h(x) are defined below:
f(x) = -2x
g(x) = 2x + 5
h(x) = x^2 + 3x - 10
Calculate the indicated function values.
1. f(a+b)
2. f(g(x))
To calculate the indicated function values, we will substitute the given expressions into the respective functions.
1. f(a+b):
Replace x in f(x) with (a+b):
f(a+b) = -2(a+b)
Simplify:
f(a+b) = -2a - 2b
2. f(g(x)):
Replace x in g(x) with x:
g(x) = 2x + 5
Replace x in f(x) with (2x + 5):
f(g(x)) = -2(2x + 5)
Simplify:
f(g(x)) = -4x - 10
To calculate the indicated function values, you need to substitute the given value or expression into the function and simplify the result. Let's go through each calculation step by step:
1. f(a+b):
To calculate f(a+b), substitute (a+b) into the function f(x):
f(a+b) = -2(a+b)
Next, simplify the expression:
f(a+b) = -2a - 2b
Therefore, the value of f(a+b) is -2a - 2b.
2. f(g(x)):
To calculate f(g(x)), substitute g(x) into the function f(x):
f(g(x)) = -2 * g(x)
Now, substitute the expression for g(x) into the equation:
f(g(x)) = -2 * (2x + 5)
Next, simplify the expression:
f(g(x)) = -4x - 10
Therefore, the value of f(g(x)) is -4x - 10.
For 1. , just replace the x with a+b
2.
f(g(x))
= f(2x+5)
= -2(2x+5)