Question

Give f(x)=x-7 and h(x)=2x+3

Write the rule for f(h(x)).

Answer 1

To find the rule for f(h(x)), you first need to substitute h(x) into the function f(x) in place of x.
Then complete the following:

Answer 2

Answer: Let’s first define the functions f(x) and h(x) as follows:

f(x) = x - 7 h(x) = 2x + 3

The rule for f(h(x)) can be obtained by substituting h(x) in place of x in the expression for f(x):

f(h(x)) = f(2x + 3)

Now, we substitute the expression for f(x) in the above equation:

f(h(x)) = (2x + 3) - 7

Simplifying the above expression, we get:

f(h(x)) = 2x - 4

Therefore, the rule for f(h(x)) is f(h(x)) = 2x - 4.