Question

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

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

Answer 1

So basically you just want to replace all the x's in the h(x) equation with the f(x) equation.

h(x-7) = 2(x-7) + 3
h(x) = 2x -14 + 3
h(x) = 2x - 11

Answer 2

h[f(x)] = 2x - 11.

Explanation:

The given functions are f(x) = x - 7 and h(x) = 2x + 3

We have to find the value of h[f(x)]

Now as per rule we will replace x of h(x) by f(x) to get the function h[f(x)].

Then function h(x) becomes as h[f(x)] and the value of the function will be

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

= 2x - 14 + 3

= 2x - 11

Therefore h[f(x)] = 2x - 11 is the answer.