Given: f(x) = x - 7 and h(x) = 2x + 3. Write the rule for h(f(x)).

Solution:

Given, f(x) = x - 7

h(x) = 2x + 3

We have to find h(f(x))

h(f(x)) = h(x - 7)

= 2(x - 7) + 3

= 2x - 14 + 3

= 2x - 11

Therefore, h(f(x)) = 2x - 11

Example: Given: f(x) = 2x - 3 and h(x) = x + 3. Write the rule for h(f(x)).

Solution:

Given, f(x) = 2x - 3

h(x) = x + 3

We have to find h(f(x))

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

= (2x - 3) + 3

= 2x - 3 + 3

= 2x - 0

= 2x

Therefore, h(f(x)) = 2x

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Given: f(x) = x - 7 and h(x) = 2x + 3. Write the rule for h(f(x)).

Summary:

Given: f(x) = x - 7 and h(x) = 2x + 3. The rule for h(f(X)) = 2x - 11.