Let's solve the problem step by step using the given functions:
Given Functions:
- $ g(x) = 3x + 1 $
- $ h(x) = x^2 + 7 $
- $ f(x) = \frac{12}{x} $
- $ j(x) = 2x + 9 $
We are asked to evaluate several expressions. Let's go through each one.
---
a. $ g(10) $
Use $ g(x) = 3x + 1 $
$$
g(10) = 3(10) + 1 = 30 + 1 = \boxed{31}
$$
---
b. $ g(3) $
$$
g(3) = 3(3) + 1 = 9 + 1 = \boxed{10}
$$
---
c. $ h(2) $
Use $ h(x) = x^2 + 7 $
$$
h(2) = (2)^2 + 7 = 4 + 7 = \boxed{11}
$$
---
d. $ j(7) $
Use $ j(x) = 2x + 9 $
$$
j(7) = 2(7) + 9 = 14 + 9 = \boxed{23}
$$
---
e. $ g(1) $
$$
g(1) = 3(1) + 1 = 3 + 1 = \boxed{4}
$$
---
f. $ h(-2) $
$$
h(-2) = (-2)^2 + 7 = 4 + 7 = \boxed{11}
$$
---
g. $ f(3) $
Use $ f(x) = \frac{12}{x} $
$$
f(3) = \frac{12}{3} = \boxed{4}
$$
---
h. $ g(10) + h(3) $
We already found $ g(10) = 31 $. Now find $ h(3) $:
$$
h(3) = (3)^2 + 7 = 9 + 7 = 16
$$
So,
$$
g(10) + h(3) = 31 + 16 = \boxed{47}
$$
---
i. $ j(4) $
$$
j(4) = 2(4) + 9 = 8 + 9 = \boxed{17}
$$
---
j. $ f(g(0)) $
This is a
composite function: first evaluate $ g(0) $, then plug that into $ f(x) $.
Step 1: $ g(0) = 3(0) + 1 = 0 + 1 = 1 $
Step 2: $ f(g(0)) = f(1) = \frac{12}{1} = \boxed{12} $
---
✔ Final Answers:
a. $ g(10) = \boxed{31} $
b. $ g(3) = \boxed{10} $
c. $ h(2) = \boxed{11} $
d. $ j(7) = \boxed{23} $
e. $ g(1) = \boxed{4} $
f. $ h(-2) = \boxed{11} $
g. $ f(3) = \boxed{4} $
h. $ g(10) + h(3) = \boxed{47} $
i. $ j(4) = \boxed{17} $
j. $ f(g(0)) = \boxed{12} $
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Parent Tip: Review the logic above to help your child master the concept of function notation practice worksheet.
