Since all options (ExplainAnswer, TeachTopic, GeneratePractice) are false, I will only provide the final answer — but per instructions, I must first work through the problem step by step and verify calculations before writing the Final Answer.
However, the user has not specified *which* problem to solve. The image contains many problems (A1–D4), each with two functions and a task (e.g., "Solve fg(x) = 21", "Solve fg(x) = g(x)", etc.).
Because no specific item is selected, and the instruction says “Solve the problem accurately”, but there are multiple problems, I must infer the most likely intent.
Looking at the structure: it's a worksheet titled “EQUATIONS THAT CONTAIN COMPOUND FUNCTIONS”, and the reference is “Ref: G285.4F1”. In many curricula (e.g., UK GCSE or A-Level), such worksheets expect students to solve *each* listed equation — but the user request says “Solve the problem”, singular.
Given the ambiguity, and since the user uploaded the full sheet but did not specify a particular cell, the safest interpretation is that they want the
first problem, A1:
> A1
> f(x) = 2x − 3
> g(x) = x² − 4
> Solve fg(x) = 21
That is, find x such that f(g(x)) = 21.
Let’s solve A1 step by step.
Step 1: Understand fg(x) means f(g(x)) — plug g(x) into f.
g(x) = x² − 4
So f(g(x)) = f(x² − 4) = 2·(x² − 4) − 3
= 2x² − 8 − 3
= 2x² − 11
Step 2: Set equal to 21:
2x² − 11 = 21
Add 11 to both sides:
2x² = 32
Divide by 2:
x² = 16
Take square roots:
x = ±4
Check:
- If x = 4: g(4) = 16 − 4 = 12; f(12) = 2·12 − 3 = 24 − 3 = 21
✔
- If x = −4: g(−4) = 16 − 4 = 12; f(12) = 21
✔
So solutions: x = 4 or x = −4.
But wait — the user may have intended a different problem. However, since no specific item was chosen, and A1 is the first, and the instruction says “the problem”, singular, standard practice is to solve the first one.
Alternatively, perhaps the user expects *all* answers? But the format要求 only one Final Answer, and options are false — meaning no explanation, no teaching, no practice — just the answer.
Given the strict instruction: “ONLY THEN provide the final answer”, and that we must reason first, I conclude the expected answer is for
A1, as it's the top-left problem.
Final Answer: x = −4 or x = 4
But how to format? Since it's a math answer, list both.
However, let me double-check if any other problem is more canonical. For example, B1: Solve fg(x) = g(x) — that’s an identity-type equation, but A1 is straightforward and labeled first.
I will go with A1.
Final Answer: x = -4, 4
Parent Tip: Review the logic above to help your child master the concept of composite function worksheet answer key.
